Methods for non-invasive prenatal paternity testing

ABSTRACT

Methods for non-invasive prenatal paternity testing are disclosed herein. The method uses genetic measurements made on plasma taken from a pregnant mother, along with genetic measurements of the alleged father, and genetic measurements of the mother, to determine whether or not the alleged father is the biological father of the fetus. This is accomplished by way of an informatics based method that can compare the genetic fingerprint of the fetal DNA found in maternal plasma to the genetic fingerprint of the alleged father.

RELATED APPLICATIONS

This application is a continuation of U.S. Utility application Ser. No.13/335,043 filed Dec. 22, 2011. U.S. Utility application Ser. No.13/335,043 claims the benefit of U.S. Provisional Application Ser. No.61/426,208, filed Dec. 22, 2010, and is a continuation-in-part of U.S.Utility application Ser. No. 13/300,235, filed Nov. 18, 2011. U.S.Utility application Ser. No. 13/300,235 claims the benefit of U.S.Provisional Application Ser. No. 61/571,248, filed Jun. 23, 2011; U.S.Provisional Application Ser. No. 61/542,508, filed Oct. 3, 2011; and isa continuation-in-part of U.S. Utility application Ser. No. 13/110,685,filed May 18, 2011. U.S. Utility application Ser. No. 13/110,685 claimsthe benefit of U.S. Provisional Application Ser. No. 61/395,850, filedMay 18, 2010; U.S. Provisional Application Ser. No. 61/398,159, filedJun. 21, 2010; U.S. Provisional Application Ser. No. 61/462,972, filedFeb. 9, 2011; U.S. Provisional Application Ser. No. 61/448,547, filedMar. 2, 2011; and U.S. Provisional Application Ser. No. 61/516,996,filed Apr. 12, 2011, and the entirety of all these applications arehereby incorporated herein by reference for the teachings therein.

FIELD

The present disclosure relates generally to methods for non-invasiveprenatal paternity testing.

BACKGROUND

Unclear parentage is a significant problem, and estimates range between4% and 10% of children who believe their biological father to be a manwho is not their actual biological father. In cases where a woman ispregnant, but relevant individuals are not sure who the biologicalfather is, there are several options to determine the correct biologicalfather of the fetus. One method is to wait until birth, and conductgenetic fingerprinting on the child and compare the genetic fingerprintof the child's genome with that of the suspected fathers. However, themother often wishes to know the identity of the biological father of herfetus prenatally. Another method is to perform chorionic villus samplingin the first trimester or amniocentesis in the second trimester, and usethe genetic material retrieved to conduct genetic fingerprintingprenatally. However, these methods are invasive, and carry a significantrisk of miscarriage.

It has recently been discovered that fetal cell-free DNA (cfDNA) andintact fetal cells can enter maternal blood circulation. Consequently,analysis of this fetal genetic material can allow early Non-InvasivePrenatal Genetic Diagnosis (NIPGD or NPD). A key challenge in performingNIPGD on fetal cells is the task of identifying and extracting fetalcells or nucleic acids from the mother's blood. The fetal cellconcentration in maternal blood depends on the stage of pregnancy andthe condition of the fetus, but estimates range from one to forty fetalcells in every milliliter of maternal blood, or less than one fetal cellper 100,000 maternal nucleated cells. Current techniques are able toisolate small quantities of fetal cells from the mother's blood,although it is difficult to enrich the fetal cells to purity in anyquantity. The most effective technique in this context involves the useof monoclonal antibodies, but other techniques used to isolate fetalcells include density centrifugation, selective lysis of adulterythrocytes, and FACS. A key challenge is performing NIPGD on fetalcfDNA is that it is typically mixed with maternal cfDNA, and thus theanalysis of the cfDNA is hindered by the need to account for thematernal genotypic signal. Fetal DNA analysis has been demonstratedusing PCR amplification using primers that are designed to hybridize tosequences that are specific to the paternally inherited genes. Thesesources of fetal genetic material open the door to non-invasive prenataldiagnostic techniques.

Once the fetal DNA has been isolated, either pure or in a mixture, itmay be amplified. There are a number of methods available for wholegenome amplification (WGA): ligation-mediated PCR (LM-PCR), degenerateoligonucleotide primer PCR (DOP-PCR), and multiple displacementamplification (MDA). There are a number of methods available fortargeted amplification including PCR, and circularizing probes such asMOLECULAR INVERSION PROBES (MIPs), and PADLOCK probes. There are othermethods that may be used for preferentially enrich fetal DNA such assize separation and hybrid capture probes.

There are numerous difficulties in using DNA amplification in thesecontexts. Amplification of single-cell DNA, DNA from a small number ofcells, or from smaller amounts of DNA, by PCR can fail completely. Thisis often due to contamination of the DNA, the loss of the cell, its DNA,or accessibility of the DNA during the amplification reaction. Othersources of error that may arise in measuring the fetal DNA byamplification and microarray analysis include transcription errorsintroduced by the DNA polymerase where a particular nucleotide isincorrectly copied during PCR, and microarray reading errors due toimperfect hybridization on the array. Another problem is allele drop-out(ADO) defined as the failure to amplify one of the two alleles in aheterozygous cell.

Many techniques exist which provide genotyping data. Some examplesinclude the following. TAQMAN is a unique genotyping technology producedand distributed by LIFE TECHNOLOGY. TAQMAN uses polymerase chainreaction (PCR) to amplify sequences of interest. AFFYMETRIX's 500KARRAYS and ILLUMINA's INFINIUM system are genotyping arrays that detectfor the presence of specific sequences of DNA at a large number oflocations simultaneously. ILLUMINA's HISEQ and MISEQ, and LIFETECHNOLOGY's ION TORRENT and SOLID platform allow the direct sequencingof a large number of individual DNA sequences.

SUMMARY

Disclosed herein are methods for determining the paternity of agestating fetus in a non-invasive manner. According to aspectsillustrated herein, in an embodiment, a method for establishing whetheran alleged father is the biological father of a fetus that is gestatingin a pregnant mother includes obtaining genetic material from thealleged father, obtaining a blood sample from the pregnant mother,making genotypic measurements, at a plurality of polymorphic loci, onthe genetic material from the alleged father, obtaining genotypicmeasurements, at the plurality of polymorphic loci, from the geneticmaterial from the pregnant mother, making genotypic measurements on amixed sample of DNA originating from the blood sample from the pregnantmother, where the mixed sample of DNA comprises fetal DNA and maternalDNA, determining, on a computer, the probability that the alleged fatheris the biological father of the fetus gestating in the pregnant motherusing the genotypic measurements made from the DNA from the allegedfather, the genotypic measurements obtained from the pregnant mother,and the genotypic measurements made on the mixed sample of DNA, andestablishing whether the alleged father is the biological father of thefetus using the determined probability that the alleged father is thebiological father of the fetus.

In an embodiment, the polymorphic loci comprise single nucleotidepolymorphisms. In an embodiment, the mixed sample of DNA comprises DNAthat was from free floating DNA in a plasma fraction of the blood samplefrom the pregnant mother. In an embodiment, the mixed sample of DNAcomprises maternal whole blood or a fraction of maternal bloodcontaining nucleated cells. In an embodiment, the fraction of maternalblood containing nucleated cells has been enriched for cells of fetalorigin.

In an embodiment, the determination of whether the alleged father is thebiological father includes calculating a test statistic for the allegedfather and the fetus, wherein the test statistic indicates a degree ofgenetic similarity between the alleged father and the fetus, and whereinthe test statistic is based on the genotypic measurements made from DNAfrom the alleged father, the genotypic measurements made from the mixedsample of DNA, and the genotypic measurements obtained from DNA from thepregnant mother, calculating a distribution of a test statistic for aplurality of individuals who are genetically unrelated to the fetus,where each calculated test statistic indicates a degree of geneticsimilarity between an unrelated individual from the plurality ofindividuals who are unrelated to the fetus and the fetus, wherein thetest statistic is based on genotypic measurements made from DNA from theunrelated individual, the genotypic measurements made from the mixedsample of DNA, and genotypic measurements obtained from DNA from thepregnant mother, calculating a probability that the test statisticcalculated for the alleged father and the fetus is part of thedistribution of the test statistic calculated for the plurality ofunrelated individuals and the fetus, and determining the probabilitythat the alleged father is the biological father of the fetus using theprobability that the test statistic calculated for the alleged father ispart of the distribution of the test statistic calculated for theplurality of unrelated individuals and the fetus. In an embodiment,establishing whether an alleged father is the biological father of thefetus also includes establishing that the alleged father is thebiological father of the fetus by rejecting a hypothesis that thealleged father is unrelated to the fetus if the probability that thealleged father is the biological father of the fetus is above an upperthreshold, or establishing that the alleged father is not the biologicalfather of the fetus by not rejecting a hypothesis that the allegedfather is unrelated to the fetus if the probability that the allegedfather is the biological father of the fetus is below a lower threshold,or not establishing whether an alleged father is the biological fatherof the fetus if the likelihood is between the lower threshold and theupper threshold, or if the likelihood was not determined withsufficiently high confidence.

In an embodiment, determining the probability that the alleged father isthe biological father of the fetus includes obtaining populationfrequencies of alleles for each locus in the plurality of polymorphicloci, creating a partition of possible fractions of fetal DNA in themixed sample of DNA that range from a lower limit of fetal fraction toan upper limit of fetal fraction, calculating a probability that thealleged father is the biological father of the fetus given the genotypicmeasurements obtained from DNA from the mother, the genotypicmeasurements made from DNA from the alleged father, the genotypicmeasurements made from the mixed sample of DNA, for each of the possiblefetal fractions in the partition, determining the probability that thealleged father is the biological father of the fetus by combining thecalculated probabilities that the alleged father is the biologicalfather of the fetus for each of the possible fetal fractions in thepartition, calculating a probability that the alleged father is not thebiological father of the fetus given the genotypic measurements madefrom DNA from the mother, the genotypic measurements made from the mixedsample of DNA, the obtained allele population frequencies; for each ofthe possible fetal fractions in the partition, and determining theprobability that the alleged father is not the biological father of thefetus by combining the calculated probabilities that the alleged fatheris not the biological father of the fetus for each of the possible fetalfractions in the partition.

In an embodiment, calculating the probability that the alleged father isthe biological father of the fetus and calculating the probability thatthe alleged father is not the biological father of the fetus may alsoinclude calculating, for each of the plurality of polymorphic loci, alikelihood of observed sequence data at a particular locus using aplatform response model, one or a plurality of fractions in the possiblefetal fractions partition, a plurality of allele ratios for the mother,a plurality of allele ratios for the alleged father, and a plurality ofallele ratios for the fetus, calculating a likelihood that the allegedfather is the biological father by combining the likelihood of theobserved sequence data at each polymorphic locus over all fetalfractions in the partition, over the mother allele ratios in the set ofpolymorphic loci, over the alleged father allele ratios in the set ofpolymorphic loci, and over the fetal allele rations in the set ofpolymorphic loci, calculating a likelihood that the alleged father isnot the biological father by combining the likelihood of the observedsequence data at each polymorphic locus over all fetal fractions in thepartition, over the mother allele ratios in the set of polymorphic loci,over population frequencies for the set of polymorphic loci, and overthe fetal allele ratios in the set of polymorphic loci, calculating aprobability that the alleged father is the biological father based onthe likelihood that the alleged father is the biological father, andcalculating a probability that the alleged father is not the biologicalfather based on the likelihood that the alleged father is not thebiological father.

In an embodiment, calculating the probability that the alleged father isthe biological father based on the likelihood that the alleged father isthe biological father is performed using a maximum likelihoodestimation, or a maximum a posteriori technique. In an embodiment,establishing whether an alleged father is the biological father of afetus may also include establishing that the alleged father is thebiological father if the calculated probability that the alleged fatheris the biological father of the fetus is significantly greater than thecalculated probability that the alleged father is not the biologicalfather, or establishing that the alleged father is not the biologicalfather of the fetus if the calculated probability that the allegedfather is the biological father is significantly greater than thecalculated probability that the alleged father is not the biologicalfather. In an embodiment, the polymorphic loci correspond to chromosomesthat have a high likelihood of being disomic.

In an embodiment, the partition of possible fractions of fetal DNAcontains only one fetal fraction, and where the fetal fraction isdetermined by a technique taken from the list consisting of quantitativePCR, digital PCR, targeted PCR, circularizing probes, other methods ofDNA amplification, capture by hybridization probes, other methods ofpreferential enrichment, SNP microarrays, DNA microarrays, sequencing,other techniques for measuring polymorphic alleles, other techniques formeasuring non-polymorphic alleles, measuring polymorphic alleles thatare present in the genome of the father but not present in the genome ofthe mother, measuring non-polymorphic alleles that are present in thegenome of the father but not present in the genome of the mother,measuring alleles that are specific to the Y-chromosome, comparing themeasured amount of paternally inherited alleles to the measured amountof maternally inherited alleles, maximum likelihood estimates, maximum aposteriori techniques, and combinations thereof. In an embodiment, themethod of claim 1, wherein the partition of possible fetal fractionscontains only one fetal fraction, and where the fetal fraction isdetermined using the method of claim 26.

In an embodiment, the alleged father's genetic material is obtained fromtissue selected from the group consisting of: blood, somatic tissue,sperm, hair, buccal sample, skin, other forensic samples, andcombinations thereof. In an embodiment, a confidence is computed for theestablished determination of whether the alleged father is thebiological father of the fetus. In an embodiment, the fraction of fetalDNA in the mixed sample of DNA has been enriched using a method selectedfrom the group consisting of: size selection, universal ligationmediated PCR, PCR with short extension times, other methods ofenrichment, and combinations thereof.

In an embodiment, obtaining genotypic measurements from the geneticmaterial of pregnant mother may include making genotypic measurements ona sample of genetic material from the pregnant mother that consistsessentially of maternal genetic material. In an embodiment, obtaininggenotypic measurements from the genetic material from the pregnantmother may include inferring which genotypic measurements from thegenotypic measurements made on the mixed sample of DNA are likelyattributable to genetic material from the pregnant mother, and usingthose genotypic measurements that were inferred to be attributable togenetic material from the mother as the obtained genotypic measurements.In an embodiment, the method may also include making a clinical decisionbased on the established paternity determination. In an embodiment, theclinical decision is to terminate a pregnancy.

In an embodiment, making genetotypic measurements may be done bymeasuring genetic material using a technique or technology selected fromthe group consisting of padlock probes, molecular inversion probes,other circularizing probes, genotyping microarrays, SNP genotypingassays, chip based microarrays, bead based microarrays, other SNPmicroarrays, other genotyping methods, Sanger DNA sequencing,pyrosequencing, high throughput sequencing, targeted sequencing usingcircularizing probes, targeted sequencing using capture by hybridizationprobes, reversible dye terminator sequencing, sequencing by ligation,sequencing by hybridization, other methods of DNA sequencing, other highthroughput genotyping platforms, fluorescent in situ hybridization(FISH), comparative genomic hybridization (CGH), array CGH, andmultiples or combinations thereof.

In an embodiment, making genotypic measurements may be done on geneticmaterial that is amplified and/or preferentially enriched prior to beingmeasured using a technique or technology that is selected from the groupconsisting of: Polymerase Chain Reaction (PCR), ligand mediated PCR,degenerative oligonucleotide primer PCR, targeted amplification, PCR,mini-PCR, universal PCR amplification, Multiple DisplacementAmplification (MDA), allele-specific PCR, allele-specific amplificationtechniques, linear amplification methods, ligation of substrate DNAfollowed by another method of amplification, bridge amplification,padlock probes, circularizing probes, capture by hybridization probes,and combinations thereof.

In an embodiment, the method may also include generating a reportcomprising the established paternity of the fetus. In an embodiment, theinvention may comprise a report disclosing the established paternity ofthe fetus generated using a method described herein.

Disclosed herein are methods for determining the fraction of DNAoriginating from a target individual is present in a mixture of DNA thatcontains DNA from the target individual, and also DNA from at least oneother individual. According to aspects illustrated herein, in anembodiment, a method for determining a fraction of DNA from a targetindividual present in a mixed sample of DNA that comprises DNA from thetarget individual and DNA from a second individual may include makinggenotypic measurements at a plurality of polymorphic loci from the mixedsample of DNA, obtaining genotypic data at the plurality of polymorphicloci from the second individual, and determining, on a computer, thefraction of DNA from the target individual present in the mixed sampleusing the genotypic measurements from the mixed sample of DNA, thegenotypic data from the second individual, and probabilistic estimationtechniques.

In an embodiment, obtaining genotypic data from the second individualincludes making genetic measurements from DNA that consists essentiallyof DNA from the second individual. In an embodiment, obtaining genotypicdata from the second individual may include inferring which genotypicmeasurements from the genotypic measurements made on the mixed sample ofDNA are likely attributable to genetic material from the secondindividual, and using those genotypic measurements that were inferred tobe attributable to genetic material from the second individual as theobtained genotypic measurements.

In an embodiment, inferring the genotypic data of the related individualmay also include using allele population frequencies at the loci. In anembodiment, the determined fraction of DNA from a target individual isexpressed as a probability of fractions of DNA. In an embodiment, thegenotypic measurements made from the mixed sample comprise genotypicmeasurements made by sequencing the DNA in the mixed sample. In anembodiment, the DNA in the mixed sample is preferentially enriched atthe plurality of polymorphic loci prior to making genotypic measurementsfrom the mixed sample of DNA. In an embodiment, the polymorphic locicomprise single nucleotide polymorphisms.

In an embodiment, determining the fraction may also include determininga probability of a plurality of fractions of DNA from the targetindividual present in the mixed sample of DNA, determining the fractionby selecting the fraction from the plurality of fractions with thelargest probability. In an embodiment, determining the fraction may alsoinclude determining a probability of a plurality of fractions of DNAfrom the target individual present in the mixed sample of DNA, using amaximum likelihood estimation technique to determine the most likelyfraction, and determining the fraction by selecting the fraction thatwas determined to be the most likely.

In an embodiment, the target individual is a fetus gestating in apregnant mother, and the second individual is the pregnant mother. In anembodiment, the method may also include using a platform model thatrelates genotypic data measured at the polymorphic loci, and using atable that relates maternal genotypes to child genotypes. In anembodiment, the determination also uses genotypic measurements at aplurality of polymorphic loci measured on DNA from the father of thefetus. In an embodiment, the method does not make use of genotypic datafrom the father of the fetus. In an embodiment, the method does not makeuse of loci on the Y chromosome. In an embodiment, the invention maycomprise a report disclosing an established paternity of the fetusdetermined using a method disclosed herein for determining the fractionof fetal DNA present in the maternal plasma. In an embodiment, theinvention may comprise a report disclosing a ploidy state of the fetusdetermined using a method disclosed herein for determining the fractionof fetal DNA present in the maternal plasma.

BRIEF DESCRIPTION OF THE DRAWINGS

The presently disclosed embodiments will be further explained withreference to the attached drawings, wherein like structures are referredto by like numerals throughout the several views. The drawings shown arenot necessarily to scale, with emphasis instead generally being placedupon illustrating the principles of the presently disclosed embodiments.

FIG. 1 shows the distribution of allele intensities from two parentalcontexts as measured on maternal plasma.

FIG. 2 shows the distribution of paternity related test statistic for200 unrelated males and the biological father.

FIG. 3 shows two distributions of intensity ratios for 200 unrelatedmales and the biological father. Each graph correspond to a differentinput channels.

FIG. 4 shows the cumulative distribution frequency (cdf) curves for thecorrelation ratio between the fetal genotypic measurements and theparental genotypic measurements for three cases.

FIG. 5 shows histograms of the correlation ratio between the fetalgenotypic measurements and the parental genotypic measurements for threecases.

FIG. 6 shows a histogram of the paternity test statistic for 35 samplesas compared to an idealized Gaussian distribution of test statistics for800 unrelated males.

FIG. 7 shows an example of a report disclosing a paternity exclusion.

FIG. 8 shows an example of a report disclosing a paternity inclusion.

FIG. 9 shows an example of a report disclosing an indeterminate result.

While the above-identified drawings set forth presently disclosedembodiments, other embodiments are also contemplated, as noted in thediscussion. This disclosure presents illustrative embodiments by way ofrepresentation and not limitation. Numerous other modifications andembodiments can be devised by those skilled in the art which fall withinthe scope and spirit of the principles of the presently disclosedembodiments.

DETAILED DESCRIPTION

According to aspects illustrated herein, a method is provided fordetermining whether or not an alleged father is the biological father ofa fetus that is gestating in a pregnant mother. In an embodiment, themethod includes obtaining genetic material from the alleged father, andobtaining a blood sample from the pregnant mother. In an embodiment, themethod may include making genotypic measurements of the alleged fatherand the pregnant mother, and making genotypic measurements on the freefloating DNA (ffDNA, i.e. cfDNA) found in the plasma of the pregnantmother. In an embodiment, the method includes obtaining genotypic datafor a set of SNPs of the mother and alleged father of the fetus; makinggenotypic measurements for the set of SNPs on a mixed sample thatcomprises DNA from the target individual and also DNA from the mother ofthe target individual. In an embodiment, the method may include usingthe genotypic measurements to determine, on a computer, the probabilitythat the alleged father is the biological father of the fetus gestatingin the pregnant mother. In an embodiment, the method may include usingthe genotypic data of the pregnant mother and the alleged father todetermine an expected allelic distribution for the genotypicmeasurements of the fetal/maternal DNA mixture if the alleged fatherwere the biological father of the fetus. In an embodiment, the methodmay include using the genotypic data of the pregnant mother andgenotypic data of a plurality of individuals known not to be the fatherto determine an expected allelic distribution for the genotypicmeasurements of the fetal/maternal DNA mixture if the alleged father isnot the biological father of the fetus. In an embodiment, the method mayinvolve calculating the probabilities that the alleged father is thebiological father of the fetus given the expected allelic distributions,and the actual maternal plasma DNA measurements. In an embodiment, theseries of steps outlined in the method results in a transformation ofthe genetic material of the pregnant mother and the alleged father toproduce and determine the correct identity of the biological father of agestating fetus prenatally and in a non-invasive manner. In anembodiment, determining the likelihood that the alleged father is thebiological father includes calling or establishing the alleged father asthe biological father if the likelihood that the father is excluded fromthe allelic distribution created using the plurality of unrelatedindividuals is above a threshold. In an embodiment, determining thelikelihood that the alleged father is the biological father includescalling the alleged father as not the biological father if thelikelihood that the alleged father is excluded from the allelicdistribution created using the plurality of unrelated individuals isbelow a threshold. In an embodiment, the paternity determination is madeby initially assuming that the alleged father is in fact the father ofthe child; if the alleged father is incorrect, the child genotypes willnot fit these predictions, and the initial assumption is considered tobe wrong; however, if the child genotypes do fit the predictions, thenthe assumption is considered to be correct. Thus, the paternity testconsiders how well the observed ffDNA fits the child genotypes predictedby the alleged father's genotypes. In an embodiment, an electronic orphysical report may be generated stating the paternity determination.

In an embodiment, the paternity determination is made using geneticmeasurements of free-floating DNA (ffDNA) found in maternal blood, andthe genotype information from the mother and alleged father. The generalmethod could be applied to measurements of ffDNA using a variety ofplatforms such as SNP microarrays, untargeted high throughputsequencing, or targeted sequencing. The methods discussed here addressthe fact that free-floating fetal DNA is found in maternal plasma at lowyet unknown concentrations and is difficult to detect. The paternitytest may comprise evaluating the ffDNA measurements and how likely theyare to have been generated by the alleged father, based on hisgenotypes. Regardless of the measurement platform, the test may be basedon the genotypes measured at polymorphic locations. In some embodimentsthe possible alleles at each polymorphic locus may be generalized to Aand B, and optionally C, D, and/or E, etc.

In an embodiment, this method involves using allele measurement datafrom a plurality of loci. In an embodiment, the loci are polymorphic. Inan embodiment, some or most of the loci are polymorphic. In anembodiment, the polymorphic loci are single nucleotide polymorphisms(SNPs). In an embodiment, some or most of the polymorphic loci areheterozygous. In an embodiment, it is not necessary to determine whichloci are heterozygous in advance of the testing.

In an embodiment, a method disclosed herein uses selective enrichmenttechniques that preserve the relative allele frequencies that arepresent in the original sample of DNA at each polymorphic locus from aset of polymorphic loci. In some embodiments the amplification and/orselective enrichment technique may involve PCR techniques such asmini-PCR or ligation mediated PCR, fragment capture by hybridization, orcircularizing probes such as Molecular Inversion Probes. In someembodiments, methods for amplification or selective enrichment mayinvolve using PCR primers or other probes where, upon correcthybridization to the target sequence, the 3-prime end or 5-prime end ofa nucleotide probe is separated from the polymorphic site of the alleleby a small number of nucleotides. In an embodiment, probes in which thehybridizing region is designed to hybridize to a polymorphic site areexcluded. These embodiments are improvements over other methods thatinvolve targeted amplification and/or selective enrichment in that theybetter preserve the original allele frequencies of the sample at eachpolymorphic locus, whether the sample is pure genomic sample from asingle individual or mixture of individuals.

In an embodiment, a method disclosed herein uses highly efficient highlymultiplexed targeted PCR to amplify DNA followed by high throughputsequencing to determine the allele frequencies at each target locus. Onetechnique that allows highly multiplexed targeted PCR to perform in ahighly efficient manner involves designing primers that are unlikely tohybridize with one another. The PCR probes may be selected by creating athermodynamic model of potentially adverse interactions, or unintendedinteractions, between at least 500, at least 1,000, at least 5,000, atleast 10,000, at least 20,000, at least 50,000, or at least 100,000potential primer pairs, or between primers and sample DNA, and thenusing the model to eliminate designs that are incompatible with otherthe designs in the pool, or with the sample DNA. Another technique thatallows highly multiplexed targeted PCR to perform in a highly efficientmanner is using a partial or full nesting approach to the targeted PCR.Using one or a combination of these approaches allows multiplexing of atleast 300, at least 800, at least 1,200, at least 4,000 or at least10,000 primers in a single pool with the resulting amplified DNAcomprising a majority of DNA molecules that, when sequenced, will map totargeted loci. Using one or a combination of these approaches allowsmultiplexing of a large number of primers in a single pool with theresulting amplified DNA comprising greater than 50%, greater than 80%,greater than 90%, greater than 95%, greater than 98%, or greater than99% DNA molecules that map to targeted loci.

In an embodiment, a method disclosed herein involves determining whetherthe distribution of observed allele measurements is indicative of apaternity inclusion or exclusion using a maximum likelihood estimation(MLE) technique. The use of a maximum likelihood estimation technique isdifferent from and a significant improvement over methods that usesingle hypothesis rejection technique in that the resultantdeterminations will be made with significantly higher accuracy. Onereason is that single hypothesis rejection techniques does not containinformation on the alternative hypothesis. Another reason is that themaximum likelihood technique allows for the determination of optimalcutoff thresholds for each individual sample. Another reason is that theuse of a maximum likelihood technique allows the calculation of aconfidence for each paternity determination. The ability to make aconfidence calculation for each determination allows a practitioner toknow which calls are accurate, and which are more likely to be wrong. Insome embodiments, a wide variety of methods may be combined with amaximum likelihood estimation technique to enhance the accuracy of theploidy calls. In an embodiment, a method disclosed herein involvesestimating the fetal fraction of DNA in the mixed sample and using thatestimation to calculate both the paternity call (determination) and theconfidence of the paternity call.

In an embodiment, the method involves calculating a test statistic thatis indicative of the degree of relatedness between a first individualand a second individual, given genotypic measurements at a plurality ofpolymorphic loci for the first individual, and genotypic measurements ata plurality of polymorphic loci for a mixture of DNA where the mixtureof DNA comprises DNA from the second individual and a relatedindividual. In an embodiment, the first individual is an alleged father,the second individual is a gestating fetus, and the related individualis the mother of the fetus. The test statistic may be calculated for thefetus, the mother, and a plurality of individuals known to be unrelatedto the fetus, thereby generating a distribution of the metric forunrelated individuals. The test statistic may also be calculated for thefetus, the mother, and the alleged father. A single hypothesis rejectiontest may be used to determine if the test statistic calculated using thealleged father's genotypic data is part of the distribution of teststatistics calculated using the genotypic data of the unrelatedindividuals. If the test statistic calculated using the alleged father'sgenotypic data is found to be part of the distribution of teststatistics calculated using the genotypic data of the unrelatedindividuals, then paternity can be excluded, that is, the alleged fathermay be determined to not be related to the fetus. If the test statisticcalculated using the alleged father's genotypic data is found not to bepart of the distribution of test statistics calculated using thegenotypic data of the unrelated individuals, then paternity can beincluded, that is, the alleged father may be determined to be related tothe fetus.

In an embodiment, the paternity determination involves determining theprobability of the measured genotypic data given two possiblehypotheses: the hypothesis that the alleged father is the biologicalfather of the fetus, and the hypothesis that the alleged father is notthe biological father of the fetus. A probability can then be calculatedfor each of the hypotheses given the data, and the paternity may beestablished based on the likelihood of each of the two hypotheses. Thedetermination may utilize genetic measurements made on the maternalplasma, genetic measurements made on DNA from the alleged father, andoptionally maternal genotypic data. In an embodiment, the maternalgenotypic data can be inferred from the genotypic measurements made onthe maternal plasma. In an embodiment, the probability can be determinedusing a partition of the range of possible fetal fractions; the range offetal fractions could be anywhere from 0.01% to 99.9%, and the mesh mayhave increments ranging from 10% to 1%, from 1% to 0.1%, and lower than0.1%. In an embodiment, the partition of possible fetal fractions may befrom 2% to 30%, and the increments are about 1%. In an embodiment, themesh could be continuous, and the likelihoods could be intergrated overthe ranges rather than combined. In an embodiment, the probability canbe determined using only one fetal fraction, where that fetal fractionmay be determined using any appropriate method. For each possible fetalfraction in the mesh, one can calculate the probability of the datagiven the two hypotheses. For the hypothesis that the alleged father isthe biological father, the alleged father genotypes may be used in thecalculation of the probability, while for the hypothesis that thealleged father is not the biological father, population based allelefrequency data may additionally be used in the calculation of theprobability. In an embodiment, one can use the parent contexts and aplatform model in calculating the likelihood of data given hypothesis.In an embodiment, the likelihoods can be combined over all fetalfractions in the partition, over all mother genotypes, and over allfather genotypes. In an embodiment, the parental genotypes may beprobabilistic (e.g. at a given SNP, a parent may have the genotype GTwith 99% chance, GG with 0.5% chance, and TT with 0.5% chance; inanother embodiment the parental genotypes may take on one value (e.g. ata given SNP, a parent has the genotype GT). In some embodiments theterms probability and likelihood may be interchangeable, as in commonparlance; in other embodiments, the two terms may not beinterchangeable, and may be read as one skilled in the art in statisticswould read them.

In some methods known in the art, fetal fraction is determined usingmeasurements made at loci that are found exclusively on the paternalgenotype, for example, loci that are found exclusively on theY-chromosome, or the Rhesus-D gene. Unfortuantely, these methods requireeither that the fetus is male (in the case where the loci are foundexclusively on the Y chromosome) or that a gene or set of genes can beidentified prior to measurements of the DNA where those genes arepresent on the paternal genotype, and not present in the maternalgenotype. An additional complication is that in the context of paternitytesting, it is not known whether or not the alleged father is thebiological father, and therefore, with the exception of the Y-chromosomespecific loci, it is not possible to determine what loci may be presenton the father, and not on the mother. Therefore, in the context ofpaternity testing, it is not currently possible to determine the fetalfraction when the fetus is a female, and when the fetus is male, fetalfraction can only be determined by using Y-chromosome specific loci. Inan embodiment, a method is disclosed herein for determining the fractionof fetal DNA that is present in the mixture of DNA comprising maternaland fetal DNA. In an embodiment, the method can determine the fetalfraction of fetal DNA that is present in the mixture of DNA comprisingmaternal and fetal DNA using genotypic measurements from autosomalchromosomes. In an embodiment, the method can determine the fetalfraction of fetal DNA that is present in the mixture of DNA comprisingmaternal and fetal DNA irrespective of the sex of the fetus. In anembodiment, the method can determine the fetal fraction of fetal DNAthat is present in the mixture of DNA comprising maternal and fetal DNAirrespective of what genes the mother and alleged father may have. Theinstant method does not require that the fetus be male, or that a locusor loci can be identified that are present on the father and not on themother. The instant method does not require that the paternal genotypebe known. The instant method does not require that the maternal genotypebe known, as it can be inferred from the measurements made on the DNA inthe maternal plasma, which comprises a mixture of both fetal andmaternal DNA.

In an embodiment, the distribution of polymorphic loci can be modeledusing a binomial distribution. In an embodiment, the distribution ofpolymorphic loci can be modeled using a beta-binomial distribution. Byusing the beta-binomial distribution as a model for allele distribution,one can more accurately model likely allele measurements than when usingother distributions; this can result in more accurate paternitydeterminations.

In an embodiment, a method disclosed herein takes into account thetendency for the data to be noisy and contain errors by attaching aprobability to each measurement. The use of maximum likelihoodtechniques to choose the correct hypothesis from the set of hypothesesthat were made using the measurement data with attached probabilisticestimates makes it more likely that the incorrect measurements will bediscounted, and the correct measurements will be used in thecalculations that lead to the paternity determination. To be moreprecise, this method systematically reduces the influence of incorrectlymeasured data on the paternity determination. This is an improvementover methods where all data is assumed to be equally correct or methodswhere outlying data is arbitrarily excluded from calculations leading toa paternity determination. In an embodiment, individual SNPs areweighted by expected measurement variance based on the SNP quality andobserved depth of read; this may result in an increase in the accuracyof the resulting statistic, resulting in an increase of the accuracy ofthe paternity call significantly, especially in borderline cases.

The methods described herein are particularly advantageous when used onsamples where a small amount of DNA is available, or where the percentof fetal DNA is low. This is due to the correspondingly higher alleledropout rate that may occur when only a small amount of DNA is availableand/or the correspondingly higher fetal allele dropout rate when thepercent of fetal DNA is low in a mixed sample of fetal and maternal DNA.A high allele dropout rate, meaning that a large percentage of thealleles were not measured for the target individual, results in poorlyaccurate fetal fraction calculations, and poorly accurate paternitydeterminations. The methods described herein allow for an accurateploidy determination to be made when the percent of molecules of DNAthat are fetal in the mixture is less than 40%, less than 30%, less than20%, less than 10%, less than 8%, less than 6%, less than 4%, and evenless than 3%.

In an embodiment, it is possible to determine the paternity of anindividual based on measurements when that individual's DNA is mixedwith DNA of a related individual. In an embodiment, the mixture of DNAis the free floating DNA found in maternal plasma, which may include DNAfrom the mother, with known genotype, and which may be mixed with DNA ofthe fetus, with unknown genotype. The paternity of the fetus can then bedetermined by looking at the actual measurements, and determining thelikelihood of paternity given the observed data. In some embodiments, amethod disclosed herein could be used in situations where there is avery small amount of DNA present, such as in forensic situations, whereone or a few cells are available (typically less than ten cells, lessthan twenty cells, less than 40 cells, less than 100 cells, or anequivalent amount of DNA.) In some embodiments, a method disclosedherein could be used in situations where the DNA is highly fragmented,such as ffDNA found in plasma. In these embodiments, a method disclosedherein serves to make paternity calls from a small amount of DNA that isnot contaminated by other DNA, but where the paternity calling verydifficult due to the small amount of DNA. The genetic measurements usedas part of these methods could be made on any sample comprising DNA orRNA, for example but not limited to: blood, plasma, body fluids, urine,hair, tears, saliva, tissue, skin, fingernails, blastomeres, embryos,amniotic fluid, chorionic villus samples, feces, bile, lymph, cervicalmucus, semen, or other cells or materials comprising nucleic acids. Inan embodiment, a method disclosed herein could be run with nucleic aciddetection methods such as sequencing, microarrays, qPCR, digital PCR, orother methods used to measure nucleic acids. In some embodiments, amethod disclosed herein involves calculating, on a computer, alleleratios at the plurality of polymorphic loci from the DNA measurementsmade on the processed samples. In some embodiments, a method disclosedherein involves calculating, on a computer, allele ratios or allelicdistributions at a plurality of polymorphic loci from the DNAmeasurements made on the processed samples along with any combination ofother improvements described in this disclosure.

Further discussion of these points may be found elsewhere in thisdocument.

Non-Invasive Prenatal Paternity Testing (NPPT)

The process of non-invasive prenatal paternity testing involves a numberof steps. Some of the steps may include: (1) obtaining the geneticmaterial from the fetus; (2) enriching the genetic material of the fetusthat may be in a mixed sample, ex vivo; (3) amplifying the geneticmaterial, ex vivo; (4) preferentially enriching specific loci in thegenetic material, ex vivo; (5) measuring the genetic material, ex vivo;and (6) analyzing the genotypic data, on a computer, and ex vivo.Methods to reduce to practice these six and other relevant steps aredescribed herein. At least some of the method steps are not directlyapplied on the body. In an embodiment, the present disclosure relates tomethods of treatment and diagnosis applied to tissue and otherbiological materials isolated and separated from the body. At least someof the method steps are executed on a computer.

Some embodiments of the present disclosure allow a clinician todetermine the genetic state of a fetus, specifically its biologicalrelationship to another individual, that is gestating in a mother in anon-invasive manner such that the health of the baby is not put at riskby the collection of the genetic material of the fetus, and that themother is not required to undergo an invasive procedure.

Modern technological advances have resulted in the ability to measurelarge amounts of genetic information from a genetic sample using suchmethods as high throughput sequencing and genotyping arrays. The methodsdisclosed herein allow a clinician to take greater advantage of thelarge amounts of data available, and make a more accurate diagnosis ofthe fetal genetic identity. In an embodiment, an informatics basedmethod may result in paternity determinations of higher accuracy than bymethods currently known in the art. The details of a number ofembodiments are given below. Different embodiments may involve differentcombinations of the aforementioned steps. Various combinations of thedifferent embodiments of the different steps may be usedinterchangeably.

In an embodiment, a blood sample is taken from a pregnant mother, andthe free floating DNA in the plasma of the mother's blood, whichcontains a mixture of both DNA of maternal origin, and DNA of fetalorigin, is isolated and used to determine the ploidy status of thefetus.

In an embodiment, a method disclosed herein involves preferentialenrichment of those DNA sequences in a mixture of DNA that correspond topolymorphic alleles in a way that the allele ratios and/or alleledistributions remain reasonably consistent upon enrichment. In anembodiment, the method involves amplifying the isolated DNA using wholegenome amplification (WGA). In an embodiment, a method disclosed hereininvolves targeted PCR based amplification such that a high percentage ofthe resulting molecules correspond to targeted loci. In an embodiment, amethod disclosed herein involves sequencing a mixture of DNA thatcontains both DNA of maternal origin, and DNA of fetal origin. In anembodiment, the method involves measuring the amplified DNA using amicroarray designed to detect nucleic acid sequences such as a SNParray. In an embodiment, a method disclosed herein involves usingmeasured allele distributions to determine the paternity of a fetus thatis gestating in a mother. In an embodiment, a method disclosed hereininvolves reporting the determined paternity state to a clinician. In anembodiment, a method disclosed herein involves taking a clinical action,for example, performing follow up invasive testing such as chorionicvillus sampling or amniocentesis, preparing for the birth of a child, oran elective termination of a fetus.

This application makes reference to U.S. Utility application Ser. No.11/603,406, filed Nov. 28, 2006 (US Publication No.: 20070184467); U.S.Utility application Ser. No. 12/076,348, filed Mar. 17, 2008 (USPublication No.: 20080243398); PCT Utility Application Serial No.PCT/US09/52730, filed Aug. 4, 2009 (PCT Publication No.:WO/2010/017214); PCT Utility Application Serial No. PCT/US10/050824,filed Sep. 30, 2010 (PCT Publication No.: WO/2011/041485), U.S. Utilityapplication Ser. No. 13/110,685, filed May 18, 2011, and U.S. Utilityapplication Ser. No. 13/300,235, filed Nov. 18, 2011. Some of thevocabulary used in this filing may have its antecedents in thesereferences. Some of the concepts described herein may be betterunderstood in light of the concepts found in these references.

Screening Maternal Blood Comprising Free Floating Fetal DNA

The methods described herein may be used to help determine whether achild, fetus, or other target individual is genetically related toanother individual. In some embodiment, this may be done in cases wherethe genetic material of the target individual is found in the presenceof a quantity of genetic material from another individual. In oneembodiment, the method may be used to help determine whether a fetus isgenetically realted to an alleged father using the free floating fetalDNA found in the maternal blood, along with a genetic sample from thefather and optionally the mother. In an embodiment, the fetus may haveoriginated from an egg from an egg donor such that the fetus is notgenetically related to the mother in which the fetus is gestating. In anembodiment, the method may be applicable in cases where the amount oftarget DNA is in any proportion with the non-target DNA; for example,the target DNA could make up anywhere between 0.000001 and 99.999999% ofthe DNA present. In an embodiment, the non-target contaminating DNAcould be from a plurality of individuals; it is advantageous wheregenetic data from some or all of the relevant non-target individual(s)is known, or where genetic samples from said related individuals areavailable. In an embodiment, a method disclosed herein can be used todetermine genotypic data of a fetus from maternal blood that containsfetal DNA. It may also be used in a case where there are multiplefetuses in the uterus of a pregnant woman, or where other contaminatingDNA may be present in the sample, for example from other already bornsiblings.

This technique may make use of the phenomenon of fetal blood cellsgaining access to maternal circulation through the placental villi.Ordinarily, only a very small number of fetal cells enter the maternalcirculation in this fashion (not enough to produce a positiveKleihauer-Betke test for fetal-maternal hemorrhage). The fetal cells canbe sorted out and analyzed by a variety of techniques to look forparticular DNA sequences, but without the risks that invasive proceduresinherently have. This technique may also make use of the phenomenon offree floating fetal DNA gaining access to maternal circulation by DNArelease following apoptosis of placental tissue where the placentaltissue in question contains DNA of the same genotype as the fetus. Thefree floating DNA found in maternal plasma has been shown to containfetal DNA in proportions as high as 30-40% fetal DNA.

In an embodiment, blood may be drawn from a pregnant woman. Research hasshown that maternal blood may contain a small amount of free floatingDNA from the fetus, in addition to free floating DNA of maternal origin.In addition, there also may be nucleated fetal blood cells comprisingDNA of fetal origin, in addition to many blood cells of maternal origin,which typically do not contain nuclear DNA. There are many methods knowin the art to isolate fetal DNA, or create fractions enriched in fetalDNA. For example, chromatography has been show to create certainfractions that are enriched in fetal DNA.

Once the sample of maternal blood, plasma, or other fluid, drawn in arelatively non-invasive manner, and that contains an amount of fetalDNA, either cellular or free floating, either enriched in its proportionto the maternal DNA, or in its original ratio, is in hand, one maygenotype the DNA found in said sample. In some embodiments, the bloodmay be drawn using a needle to withdraw blood from a vein, for example,the basilica vein. The method described herein can be used to determinegenotypic data of the fetus. For example, it can be used to determinethe ploidy state at one or more chromosomes, it can be used to determinethe identity of one or a set of SNPs, including insertions, deletions,and translocations. It can be used to determine one or more haplotypes,including the parent of origin of one or more genotypic features. It canalso be used to determine the degree of relatedness between the fetus ananother individual.

Note that this method will work with any nucleic acids that can be usedfor any genotyping and/or sequencing methods, such as the ILLUMINAINFINIUM ARRAY platform, AFFYMETRIX GENECHIP, ILLUMINA GENOME ANALYZER,or LIFE TECHNOLOGIES' SOLID SYSTEM, along with the genotypic datameasured therefrom. This includes extracted free-floating DNA fromplasma or amplifications (e.g. whole genome amplification, PCR) of thesame; genomic DNA from other cell types (e.g. human lymphocytes fromwhole blood) or amplifications of the same. For preparation of the DNA,any extraction or purification method that generates genomic DNAsuitable for the one of these platforms will work as well. This methodcould work equally well with samples of RNA. In an embodiment, storageof the samples may be done in a way that will minimize degradation (e.g.below freezing, at about −20 C, or at a lower temperature).

Parental Support

Some embodiments may be used in combination with the PARENTAL SUPPORT™(PS) method, embodiments of which are described in U.S. application Ser.No. 11/603,406 (US Publication No.: 20070184467), U.S. application Ser.No. 12/076,348 (US Publication No.: 20080243398), U.S. application Ser.No. 13/110,685, PCT Application PCT/US09/52730 (PCT Publication No.:WO/2010/017214), PCT Application No. PCT/US10/050824 (PCT PublicationNo.: WO/2011/041485), PCT Application No. PCT/US2011/037018 (PCTPublication No.: WO/2011/146632), and PCT Application No.PCT/US2011/61506, which are incorporated herein by reference in theirentirety. PARENTAL SUPPORT™ is an informatics based approach that can beused to analyze genetic data. In some embodiments, the methods disclosedherein may be considered as part of the PARENTAL SUPPORT™ method. Insome embodiments, The PARENTAL SUPPORT™ method is a collection ofmethods that may be used to determine the genetic data of a targetindividual, with high accuracy, of one or a small number of cells fromthat individual, or of a mixture of DNA consisting of DNA from thetarget individual and DNA from one or a plurality of other individuals,specifically to determine disease-related alleles, other alleles ofinterest, the ploidy state of one or a plurality of chromosomes in thetarget individual, and or the extent of relationship of anotherindividual to the target individual. PARENTAL SUPPORT™ may refer to anyof these methods. PARENTAL SUPPORT™ is an example of an informaticsbased method.

The PARENTAL SUPPORT™ method makes use of known parental genetic data,i.e. haplotypic and/or diploid genetic data of the mother and/or thefather, together with the knowledge of the mechanism of meiosis and theimperfect measurement of the target DNA, and possibly of one or morerelated individuals, along with population based crossover frequencies,in order to reconstruct, in silico, the genotype at a plurality ofalleles, and/or the paternity state of an embryo or of any targetcell(s), and the target DNA at the location of key loci with a highdegree of confidence. The PARENTAL SUPPORT™ method makes use of knownparental genetic data, i.e. haplotypic and/or diploid genetic data ofthe mother and/or the father, together with the knowledge of themechanism of meiosis and the imperfect measurement of the target DNA, tocreate hypotheses about what genetic data may be expected for differentsituations, to calculate the likelihood of each of the situations giventhe observed genetic data, thereby determining which situation is mostlikely. In some embodiments the situation is question may includewhether the target individual has inherited a disease linked haplotypeof interest, whether the target individual has inherited a phenotypelinked haplotype of interest, whether the target individual has one ormore aneuploid chromosomes, and/or whether the target individual isrelated to an individual of interest, and what the degree ofrelationship may be. The PARENTAL SUPPORT™ method allows the cleaning ofnoisy genetic data. PARENTAL SUPPORT™ may be particularly relevant whereonly a small fraction of the genetic material available is from thetarget individual (e.g. NPD or NPPT) and where direct measurements ofthe genotypes are inherently noisy due to the contaminating DNA signalfrom another individual. The PARENTAL SUPPORT™ method is able toreconstruct highly accurate ordered diploid allele sequences on theembryo, together with copy number of chromosomes segments, even thoughthe conventional, unordered diploid measurements may be characterized byhigh rates of allele dropouts, drop-ins, variable amplification biasesand other errors. The method may employ both an underlying genetic modeland an underlying model of measurement error. The genetic model maydetermine both allele probabilities at each SNP and crossoverprobabilities between SNPs. Allele probabilities may be modeled at eachSNP based on data obtained from the parents and model crossoverprobabilities between SNPs based on data obtained from the HapMapdatabase, as developed by the International HapMap Project. Given theproper underlying genetic model and measurement error model, maximum aposteriori (MAP) estimation may be used, with modifications forcomputationally efficiency, to estimate the correct, ordered allelevalues at each SNP in the embryo.

Definitions

-   Single Nucleotide Polymorphism (SNP) refers to a single nucleotide    that may differ between the genomes of two members of the same    species. The usage of the term should not imply any limit on the    frequency with which each variant occurs.-   Sequence refers to a DNA sequence or a genetic sequence. It may    refer to the primary, physical structure of the DNA molecule or    strand in an individual. It may refer to the sequence of nucleotides    found in that DNA molecule, or the complementary strand to the DNA    molecule. It may refer to the information contained in the DNA    molecule as its representation in silico.-   Locus refers to a particular region of interest on the DNA of an    individual, which may refer to a SNP, the site of a possible    insertion or deletion, or the site of some other relevant genetic    variation. Disease-linked SNPs may also refer to disease-linked    loci.-   Polymorphic Allele, also “Polymorphic Locus,” refers to an allele or    locus where the genotype varies between individuals within a given    species. Some examples of polymorphic alleles include single    nucleotide polymorphisms, short tandem repeats, deletions,    duplications, and inversions.-   Polymorphic Site refers to the specific nucleotides found in a    polymorphic region that vary between individuals.-   Allele refers to the genes that occupy a particular locus.-   Genetic Data also “Genotypic Data” refers to the data describing    aspects of the genome of one or more individuals. It may refer to    one or a set of loci, partial or entire sequences, partial or entire    chromosomes, or the entire genome. It may refer to the identity of    one or a plurality of nucleotides; it may refer to a set of    sequential nucleotides, or nucleotides from different locations in    the genome, or a combination thereof. Genotypic data is typically in    silico, however, it is also possible to consider physical    nucleotides in a sequence as chemically encoded genetic data.    Genotypic Data may be said to be “on,” “of,” “at,” “from” or “on”    the individual(s). Genotypic Data may refer to output measurements    from a genotyping platform where those measurements are made on    genetic material.-   Genetic Material also “Genetic Sample” refers to physical matter,    such as tissue or blood, from one or more individuals comprising DNA    or RNA-   Confidence refers to the statistical likelihood that the called SNP,    allele, set of alleles, ploidy call, or paternity call is correct.-   Aneuploidy refers to the state where the wrong number of chromosomes    is present in a cell. In the case of a somatic human cell it may    refer to the case where a cell does not contain 22 pairs of    autosomal chromosomes and one pair of sex chromosomes. In the case    of a human gamete, it may refer to the case where a cell does not    contain one of each of the 23 chromosomes. In the case of a single    chromosome type, it may refer to the case where more or less than    two homologous but non-identical chromosome copies are present, or    where there are two chromosome copies present that originate from    the same parent.-   Chromosome may refer to a single chromosome copy, meaning a single    molecule of DNA of which there are 46 in a normal somatic cell; an    example is ‘the maternally derived chromosome 18’. Chromosome may    also refer to a chromosome type, of which there are 23 in a normal    human somatic cell; an example is ‘chromosome 18’.-   Monosomy refers to the state where a cell only contains one of a    chromosome type.-   Disomy refers to the state where a cell contains two of a chromosome    type.-   Uniparental Disomy refers to the state where a cell contains two of    a chromosome type, and where both chromosomes originate from one    parent.-   Trisomy refers to the state where a cell contains three of a    chromosome type.-   The State of the Genetic Material or simply “Genetic State” may    refer to the identity of a set of SNPs on the DNA, to the phased    haplotypes of the genetic material, or to the sequence of the DNA,    including insertions, deletions, repeats and mutations. It may also    refer to the ploidy state of one or more chromosomes, chromosomal    segments, or set of chromosomal segments.-   Establishing the Paternity or “Determining the Paternity” refers to    establishing or determining that an alleged father either is or is    not the biological father of a gestating fetus, or determining or    establishing the likelihood that an alleged father is the biological    father of the fetus.-   Paternity Determination refers to the determination that the alleged    father is or is not the biological father of the fetus. A paternity    determination is the result of establishing, calling or determining    the paternity.-   Paternity refers to the identity of the biological father of an    individual.-   Paternity Inclusion refers to establishing that an alleged father is    the biological father of a fetus.-   Paternity Exclusion refers to establishing that an alleged father is    not the biological father of a fetus.-   Alleged Father refers to a male whose paternal relationship to a    fetus is in question.-   Biological Father of an individual refers to the male whose genetic    material was inherited by the individual.-   Allelic Ratio refers to the ratio between the amount of each allele    at a polymorphic locus that is present in a sample or in an    individual. When the sample is measured by sequencing, the allelic    ratio may refer to the ratio of sequence reads that map to each    allele at the locus. When the sample is measured by an intensity    based measurement method, the allele ratio may refer to the ratio of    the amounts of each allele present at that locus as estimated by the    measurement method.-   Allelic Distribution, or ‘allele count distribution’ refers to the    relative amount of each allele that is present for each locus in a    set of loci. An allelic distribution can refer to an individual, to    a sample, or to a set of measurements made on a sample. In the    context of sequencing, the allelic distribution refers to the number    or probable number of reads that map to a particular allele for each    allele in a set of polymorphic loci. The allele measurements may be    treated probabilistically, that is, the likelihood that a given    allele is present for a give sequence read is a fraction between 0    and 1, or they may be treated in a binary fashion, that is, any    given read is considered to be exactly zero or one copies of a    particular allele.-   Allelic Bias refers to the degree to which the measured ratio of    alleles at a heterozygous locus is different to the ratio that was    present in the original sample of DNA. The degree of allelic bias at    a particular locus is equal to the observed allelelic ratio at that    locus, as measured, divided by the ratio of alleles in the original    DNA sample at that locus. Allelic bias may be defined to be greater    than one, such that if the calculation of the degree of allelic bias    returns a value, x, that is less than 1, then the degree of allelic    bias may be restated as 1/x. Allelic bias maybe due to amplification    bias, purification bias, or some other phenomenon that affects    different alleles differently.-   Primer, also “PCR probe” refers to a single DNA molecule (a DNA    oligomer) or a collection of DNA molecules (DNA oligomers) where the    DNA molecules are identical, or nearly so, and where the primer    contains a region that is designed to hybridize to a targeted    polymorphic locus, and may contain a priming sequence designed to    allow PCR amplification. A primer may also contain a molecular    barcode. A primer may contain a random region that differs for each    individual molecule.-   Hybrid Capture Probe refers to any nucleic acid sequence, possibly    modified, that is generated by various methods such as PCR or direct    synthesis and intended to be complementary to one strand of a    specific target DNA sequence in a sample. The exogenous hybrid    capture probes may be added to a prepared sample and hybridized    through a deanture-reannealing process to form duplexes of    exogenous-endogenous fragments. These duplexes may then be    physically separated from the sample by various means.-   Sequence Read refers to data representing a sequence of nucleotide    bases that were measured using a clonal sequencing method. Clonal    sequencing may produce sequence data representing single, or clones,    or clusters of one original DNA molecule. A sequence read may also    have associated quality score at each base position of the sequence    indicating the probability that nucleotide has been called    correctly.-   Mapping a sequence read is the process of determining a sequence    read's location of origin in the genome sequence of a particular    organism. The location of origin of sequence reads is based on    similarity of nucleotide sequence of the read and the genome    sequence.-   Homozygous refers to having similar alleles at corresponding    chromosomal loci.-   Heterozygous refers to having dissimilar alleles at corresponding    chromosomal loci.-   Heterozygosity Rate refers to the rate of individuals in the    population having heterozygous alleles at a given locus. The    heterozygosity rate may also refer to the expected or measured ratio    of alleles, at a given locus in an individual, or a sample of DNA.-   Haplotype refers to a combination of alleles at multiple loci that    are typically inherited together on the same chromosome. Haplotype    may refer to as few as two loci or to an entire chromosome depending    on the number of recombination events that have occurred between a    given set of loci. Haplotype can also refer to a set of single    nucleotide polymorphisms (SNPs) on a single chromatid that are    statistically associated.-   Haplotypic Data, also “Phased Data” or “Ordered Genetic Data,”    refers to data from a single chromosome in a diploid or polyploid    genome, i.e., either the segregated maternal or paternal copy of a    chromosome in a diploid genome.-   Phasing refers to the act of determining the haplotypic genetic data    of an individual given unordered, diploid (or polyploid) genetic    data. It may refer to the act of determining which of two genes at    an allele, for a set of alleles found on one chromosome, are    associated with each of the two homologous chromosomes in an    individual.-   Phased Data refers to genetic data where one or more haplotypes have    been determined.-   Fetal refers to “of the fetus,” or “of the region of the placenta    that is genetically similar to the fetus”. In a pregnant woman, some    portion of the placenta is genetically similar to the fetus, and the    free floating fetal DNA found in maternal blood may have originated    from the portion of the placenta with a genotype that matches the    fetus.-   DNA of Fetal Origin refers to DNA that was originally part of a cell    whose genotype was essentially equivalent to that of the fetus. Note    that the genetic information in half of the chromosomes in a fetus    is inherited from the mother of the fetus; in some embodiments, the    DNA from these maternally inherited chromosomes that came from a    fetal cell is considered to be “of fetal origin,” and not “of    maternal origin.”-   DNA of Maternal Origin refers to DNA that was originally part of a    cell whose genotype was essentially equivalent to that of the    mother.-   Child may refer to an embryo, a blastomere, or a fetus. Note that in    the presently disclosed embodiments, the concepts described apply    equally well to individuals who are a born child, a fetus, an embryo    or a set of cells therefrom. The use of the term child may simply be    meant to connote that the individual referred to as the child is the    genetic offspring of the parents.-   Parent refers to the genetic mother or father of an individual. An    individual typically has two parents, a mother and a father, though    this may not necessarily be the case such as in genetic or    chromosomal chimerism.-   Mother may refer to the biological mother of an individual, and/or    it may refer to the women who is carrying the individual as he/she    gestates.-   Parental Context refers to the genetic state of a given SNP, on each    of the two relevant chromosomes for one or both of the two parents    of the target.-   Maternal Plasma refers to the plasma portion of the blood from a    female who is pregnant.-   Clinical Decision refers to any decision to take or not take an    action that has an outcome that affects the health or survival of an    individual. In the context of prenatal paternity testing, a clinical    decision may refer to a decision to abort or not abort a fetus. A    clinical decision may also refer to a decision to conduct further    testing, or to take actions to prepare for the birth of a child.-   Diagnostic Box refers to one or a combination of machines designed    to perform one or a plurality of aspects of the methods disclosed    herein. In an embodiment, the diagnostic box may be placed at a    point of patient care. In an embodiment, the diagnostic box may    perform targeted amplification followed by sequencing. In an    embodiment the diagnostic box may function alone or with the help of    a technician.-   Informatics Based Method or ‘informatics based approach’ refers to a    method that relies heavily on statistics to make sense of a large    amount of data. In the context of prenatal diagnosis, it refers to a    method designed to determine the ploidy state at one or more    chromosomes or the allelic state at one or more alleles by    statistically inferring the most likely state, rather than by    directly physically measuring the state, given a large amount of    genetic data, for example from a molecular array or sequencing. In    an embodiment of the present disclosure, the informatics based    technique may be one disclosed in this patent. In an embodiment of    the present disclosure it may be PARENTAL SUPPORT™.-   Preferential Enrichment of DNA that corresponds to one or a    plurality of loci, or preferential enrichment of DNA at one or a    plurality of loci, refers to any method that results in the    percentage of molecules of DNA in a post-enrichment DNA mixture that    correspond to the loci being higher than the percentage of molecules    of DNA in the pre-enrichment DNA mixture that correspond to the    loci. The method may involve selective amplification of DNA    molecules that correspond to the loci. The method may involve    removing DNA molecules that do not correspond to the loci.-   Amplification refers to a method that increases the number of copies    of a molecule of DNA.-   Selective Amplification may refer to a method that increases the    number of copies of a particular molecule of DNA, or molecules of    DNA that correspond to a particular region of DNA. It may also refer    to a method that increases the number of copies of a particular    targeted molecule of DNA, or targeted region of DNA more than it    increases non-targeted molecules or regions of DNA. Selective    amplification may be a method of preferential enrichment.-   Universal Priming Sequence refers to a DNA sequence that may be    appended to a population of target DNA molecules, for example by    ligation, PCR, or ligation mediated PCR. Once added to the    population of target molecules, primers specific to the universal    priming sequences can be used to amplify the target population using    a single pair of amplification primers. Universal priming sequences    are typically not related to the target sequences.-   Universal Adapters, or ‘ligation adaptors’ or ‘library tags’ are DNA    molecules containing a universal priming sequence that can be    covalently linked to the 5-prime and 3-prime end of a population of    target double stranded DNA molecules. The addition of the adapters    provides universal priming sequences to the 5-prime and 3-prime end    of the target population from which PCR amplification can take    place, amplifying all molecules from the target population, using a    single pair of amplification primers.-   Targeting refers to a method used to selectively amplify or    otherwise preferentially enrich those molecules of DNA that    correspond to a set of loci, in a mixture of DNA.-   Hypothesis refers to the possibility that the alleged father is the    biological father of the fetus, or that the alleged father is not    the biological father of the fetus.-   Determining, establishing, and calculating may be used    interchangeably.    Parental Contexts

The parental context refers to the genetic state of a given allele, oneach of the two relevant chromosomes for one or both of the two parentsof the target. Note that in an embodiment, the parental context does notrefer to the allelic state of the target, rather, it refers to theallelic state of the parents. The parental context for a given SNP mayconsist of four base pairs, two paternal and two maternal; they may bethe same or different from one another. It is typically written as“m₁m₂|f₁f₂,” where m₁ and m₂ are the genetic state of the given SNP onthe two maternal chromosomes, and f₁ and f₂ are the genetic state of thegiven SNP on the two paternal chromosomes. In some embodiments, theparental context may be written as “f₁f₂|m₁m₂.” Note that subscripts “1”and “2” refer to the genotype, at the given allele, of the first andsecond chromosome; also note that the choice of which chromosome islabeled “1” and which is labeled “2” may be arbitrary.

Note that in this disclosure, A and B are often used to genericallyrepresent base pair identities; A or B could equally well represent C(cytosine), G (guanine), A (adenine) or T (thymine). For example, if, ata given SNP based allele, the mother's genotype was T at that SNP on onechromosome, and G at that SNP on the homologous chromosome, and thefather's genotype at that allele is G at that SNP on both of thehomologous chromosomes, one may say that the target individual's allelehas the parental context of AB|BB; it could also be said that the allelehas the parental context of AB|AA. Note that, in theory, any of the fourpossible nucleotides could occur at a given allele, and thus it ispossible, for example, for the mother to have a genotype of AT, and thefather to have a genotype of GC at a given allele. However, empiricaldata indicate that in most cases only two of the four possible basepairs are observed at a given allele. It is possible, for example whenusing single tandem repeats, to have more than two parental, more thanfour and even more than ten contexts. In this disclosure the discussionassumes that only two possible base pairs will be observed at a givenallele, although the embodiments disclosed herein could be modified totake into account the cases where this assumption does not hold.

A “parental context” may refer to a set or subset of target SNPs thathave the same parental context. For example, if one were to measure 1000alleles on a given chromosome on a target individual, then the contextAA|BB could refer to the set of all alleles in the group of 1,000alleles where the genotype of the mother of the target was homozygous,and the genotype of the father of the target is homozygous, but wherethe maternal genotype and the paternal genotype are dissimilar at thatlocus. If the parental data is not phased, and thus AB=BA, then thereare nine possible parental contexts: AA|AA, AA|AB, AA|BB, AB|AA, AB|AB,AB|BB, BB|AA, BB|AB, and BB|BB. If the parental data is phased, and thusAB≠BA, then there are sixteen different possible parental contexts:AA|AA, AA|AB, AA|BA, AA|BB, AB|AA, AB|AB, AB|BA, AB|BB, BA|AA, BA|AB,BA|BA, BA|BB, BB|AA, BB|AB, BB|BA, and BB|BB. Every SNP allele on achromosome, excluding some SNPs on the sex chromosomes, has one of theseparental contexts. The set of SNPs wherein the parental context for oneparent is heterozygous may be referred to as the heterozygous context.

Different Implementations of the Presently Disclosed Embodiments

Method are disclosed herein for determining the paternity of a targetindividual. The target individual may be a blastomere, an embryo, or afetus. In some embodiments of the present disclosure, a method fordetermining the paternity of an individual may include any of the stepsdescribed in this document, and combinations thereof:

In some embodiments the source of the genetic material to be used indetermining the paternity of the fetus may be fetal cells, such asnucleated fetal red blood cells, isolated from the maternal blood. Themethod may involve obtaining a blood sample from the pregnant mother. Insome embodiments of the present disclosure, the genetic material to beused in determining the paternity of the fetus may free floating DNAfrom maternal plasma, where the free floating DNA may be comprised of amixture of fetal and maternal DNA.

In some embodiments, the source of the genetic material of the fetus maybe fetal cells, such as nucleated fetal red blood cells, isolated fromthe maternal blood. The method may involve obtaining a blood sample fromthe pregnant mother. The method may involve isolating a fetal red bloodcell using visual techniques, based on the idea that a certaincombination of colors are uniquely associated with nucleated red bloodcell, and a similar combination of colors is not associated with anyother present cell in the maternal blood. The combination of colorsassociated with the nucleated red blood cells may include the red colorof the hemoglobin around the nucleus, which color may be made moredistinct by staining, and the color of the nuclear material which can bestained, for example, blue. By isolating the cells from maternal bloodand spreading them over a slide, and then identifying those points atwhich one sees both red (from the Hemoglobin) and blue (from the nuclearmaterial) one may be able to identify the location of nucleated redblood cells. One may then extract those nucleated red blood cells usinga micromanipulator, use genotyping and/or sequencing techniques tomeasure aspects of the genotype of the genetic material in those cells.

In one embodiment, one may stain the nucleated red blood cell with a diethat only fluoresces in the presence of fetal hemoglobin and notmaternal hemoglobin, and so remove the ambiguity between whether anucleated red blood cell is derived from the mother or the fetus. Someembodiments of the present disclosure may involve staining or otherwisemarking nuclear material. Some embodiments of the present disclosure mayinvolve specifically marking fetal nuclear material using fetal cellspecific antibodies.

There are many other ways to isolate fetal cells from maternal blood, orfetal DNA from maternal blood, or to enrich samples of fetal geneticmaterial in the presence of maternal genetic material. Some of thesemethods are listed here, but this is not intended to be an exhaustivelist. Some appropriate techniques are listed here for convenience: usingfluorescently or otherwise tagged antibodies, size exclusionchromatography, magnetically or otherwise labeled affinity tags,epigenetic differences, such as differential methylation between thematernal and fetal cells at specific alleles, density gradientcentrifugation succeeded by CD45/14 depletion and CD71-positiveselection from CD45/14 negative-cells, single or double Percollgradients with different osmolalities, or galactose specific lectinmethod.

In some embodiments, the genetic sample may be prepared, isolated and/orpurified. In some embodiments, the sample may be centrifuged to separatevarious layers. In some embodiments the preparation of the DNA mayinvolve amplification, separation, purification by chromatography,purification by electrophoresis, filtration, liquid separation,isolation, precipitation, preferential enrichment, preferentialamplification, targeted amplification, or any of a number of othertechniques either known in the art or described herein.

In some embodiments, the method of the present disclosure may involveamplifying DNA. Amplification of the DNA, a process which transforms asmall amount of genetic material to a larger amount of genetic materialthat comprises a similar set of genetic data, can be done by a widevariety of methods, including, but not limited to polymerase chainreaction (PCR). One method of amplifying DNA is whole genomeamplification (WGA). There are a number of methods available for WGA:ligation-mediated PCR (LM-PCR), degenerate oligonucleotide primer PCR(DOP-PCR), and multiple displacement amplification (MDA). In LM-PCR,short DNA sequences called adapters are ligated to blunt ends of DNA.These adapters contain universal amplification sequences, which are usedto amplify the DNA by PCR. In DOP-PCR, random primers that also containuniversal amplification sequences are used in a first round of annealingand PCR. Then, a second round of PCR is used to amplify the sequencesfurther with the universal primer sequences. MDA uses the phi-29polymerase, which is a highly processive and non-specific enzyme thatreplicates DNA and has been used for single-cell analysis. Single-cellwhole genome amplification has been used successfully for a variety ofapplications for a number of years. There are other methods ofamplifying DNA from a sample of DNA. The DNA amplification transformsthe initial sample of DNA into a sample of DNA that is similar in theset of sequences, but of much greater quantities. In some cases,amplification may not be required.

In some embodiments, DNA may be amplified using a universalamplification, such as WGA or MDA. In some embodiments, DNA may beamplified by targeted amplification, for example using targeted PCR, orcircularizing probes. In some embodiments, the DNA may be preferentiallyenriched using a targeted amplification method, or a method that resultsin the full or partial separation of desired from undesired DNA, such ascapture by hybridization approaches. In some embodiments, DNA may beamplified by using a combination of a universal amplification method anda preferential enrichment method. A fuller description of some of thesemethods can be found elsewhere in this document.

The genetic data of the target individual and/or of the relatedindividual can be transformed from a molecular state to an electronicstate by measuring the appropriate genetic material using tools and ortechniques taken from a group including, but not limited to:

genotyping microarrays, and high throughput sequencing. Some highthroughput sequencing methods include Sanger DNA sequencing,pyrosequencing, the ILLUMINA SOLEXA platform, ILLUMINA's GENOMEANALYZER, or APPLIED BIOSYSTEM's 454 sequencing platform, HELICOS's TRUESINGLE MOLECULE SEQUENCING platform, HALCYON MOLECULAR's electronmicroscope sequencing method, or any other sequencing method. All ofthese methods physically transform the genetic data stored in a sampleof DNA into a set of genetic data that is typically stored in a memorydevice en route to being processed.

A relevant individual's genetic data may be measured by analyzingsubstances taken from a group including, but not limited to: theindividual's bulk diploid tissue, one or more diploid cells from theindividual, one or more haploid cells from the individual, one or moreblastomeres from the target individual, extra-cellular genetic materialfound on the individual, extra-cellular genetic material from theindividual found in maternal blood, cells from the individual found inmaternal blood, one or more embryos created from a gamete from therelated individual, one or more blastomeres taken from such an embryo,extra-cellular genetic material found on the related individual, geneticmaterial known to have originated from the related individual, andcombinations thereof.

In some embodiments, the likelihood that an alleged father is thebiological father of a fetus may be calculated. In some embodiments, thepaternity determination may be used to make a clinical decision. Thisknowledge, typically stored as a physical arrangement of matter in amemory device, may then be transformed into a report. The report maythen be acted upon. For example, the clinical decision may be toterminate the pregnancy; alternately, the clinical decision may be tocontinue the pregnancy.

In an embodiment of the present disclosure, any of the methods describedherein may be modified to allow for multiple targets to come from sametarget individual, for example, multiple blood draws from the samepregnant mother. This may improve the accuracy of the model, as multiplegenetic measurements may provide more data with which the targetgenotype may be determined. In an embodiment, one set of target geneticdata served as the primary data which was reported, and the other servedas data to double-check the primary target genetic data. In anembodiment, a plurality of sets of genetic data, each measured fromgenetic material taken from the target individual, are considered inparallel, and thus both sets of target genetic data serve to helpdetermine the paternity of the fetus.

In an embodiment, the method may be used for the purpose of paternitytesting. For example, given the SNP-based genotypic information from themother, and from a man who may or may not be the genetic father, and themeasured genotypic information from the mixed sample, it is possible todetermine if the genotypic information of the male indeed representsthat actual genetic father of the gestating fetus. A simple way to dothis is to simply look at the contexts where the mother is AA, and thepossible father is AB or BB. In these cases, one may expect to see thefather contribution half (AA|AB) or all (AA|BB) of the time,respectively. Taking into account the expected ADO, it isstraightforward to determine whether or not the fetal SNPs that areobserved are correlated with those of the possible father. Other methodsfor making a paternity determination are described elsewhere in thisdocument.

In an embodiment of the present disclosure, a pregnant mother would liketo determine if a man is the biological father of her fetus. She goes toher doctor, and gives a sample of her blood, and she and her husbandgives samples of their own DNA from cheek swabs. A laboratory researchergenotypes the parental DNA using the MDA protocol to amplify theparental DNA, and ILLUMINA INFINIUM arrays to measure the genetic dataof the parents at a large number of SNPs. The researcher then spins downthe blood, takes the plasma, and isolates a sample of free-floating DNAusing size exclusion chromatography. Alternately, the researcher usesone or more fluorescent antibodies, such as one that is specific tofetal hemoglobin to isolate a nucleated fetal red blood cell. Theresearcher then takes the isolated or enriched fetal genetic materialand amplifies it using a library of 70-mer oligonucleotidesappropriately designed such that two ends of each oligonucleotidecorresponded to the flanking sequences on either side of a targetallele. Upon addition of a polymerase, ligase, and the appropriatereagents, the oligonucleotides underwent gap-filling circularization,capturing the desired allele. An exonuclease was added,heat-inactivated, and the products were used directly as a template forPCR amplification. The PCR products were sequenced on an ILLUMINA GENOMEANALYZER. The sequence reads were used as input for the PARENTALSUPPORT™ method, which then predicted the ploidy state of the fetus. Themethod determines that the alleged father is not the biological fatherof the fetus, and calculates a confidence on the determination of99.98%. A report is generated disclosing both the paternitydetermination and the confidence of the determination.

In another embodiment a woman who is pregnant wants to know if a man isthe biological father of her fetus. The obstetrician takes a blood drawfrom the mother and father. The blood is sent to a laboratory, where atechnician centrifuges the maternal sample to isolate the plasma and thebuffy coat. The DNA in the buffy coat and the paternal blood sample aretransformed through amplification and the genetic data encoded in theamplified genetic material is further transformed from molecularlystored genetic data into electronically stored genetic data by runningthe genetic material on a high throughput sequencer to measure theparental genotypes. The plasma sample is preferentially enriched at aset of loci using a 5,000-plex hemi-nested targeted PCR method. Themixture of DNA fragments is prepared into a DNA library suitable forsequencing. The DNA is then sequenced using a high throughput sequencingmethod, for example, the ILLUMINA GAIIx GENOME ANALYZER. The sequencingtransforms the information that is encoded molecularly in the DNA intoinformation that is encoded electronically in computer hardware. Aninformatics based technique that includes the presently disclosedembodiments, such as PARENTAL SUPPORT™, may be used to determine thepaternity of the fetus. This may involve calculating, on a computer,allele counts at the plurality of polymorphic loci from the DNAmeasurements made on the enriched sample; and determining the likelihoodthat the man is the biological father of her fetus. The probability thatthe alleged father is the biological father of the fetus is determinedto be 99.9999%, and the confidence of the paternity determination iscalculated to be 99.99%. A report is printed out, or sent electronicallyto the pregnant woman's obstetrician, who transmits the determination tothe woman. The woman, her husband, and the doctor sit down and discussthe report.

In an embodiment, the raw genetic material of the mother and the fatheris transformed by way of amplification to an amount of DNA that issimilar in sequence, but larger in quantity. Then, by way of agenotyping method, the genotypic data that is encoded by nucleic acidsis transformed into genetic measurements that may be stored physicallyand/or electronically on a memory device, such as those described above.The relevant algorithms that makeup the PARENTAL SUPPORT™ algorithm,relevant parts of which are discussed in detail herein, are translatedinto a computer program, using a programming language. Then, through theexecution of the computer program on the computer hardware, instead ofbeing physically encoded bits and bytes, arranged in a pattern thatrepresents raw measurement data, they become transformed into a patternthat represents a high confidence determination of the paternity of thefetus. The details of this transformation will rely on the data itselfand the computer language and hardware system used to execute the methoddescribed herein. Then, the data that is physically configured torepresent a high quality paternity determination of the fetus istransformed into a report which may be sent to a health carepractitioner. This transformation may be carried out using a printer ora computer display. The report may be a printed copy, on paper or othersuitable medium, or else it may be electronic. In the case of anelectronic report, it may be transmitted, it may be physically stored ona memory device at a location on the computer accessible by the healthcare practitioner; it also may be displayed on a screen so that it maybe read. In the case of a screen display, the data may be transformed toa readable format by causing the physical transformation of pixels onthe display device. The transformation may be accomplished by way ofphysically firing electrons at a phosphorescent screen, by way ofaltering an electric charge that physically changes the transparency ofa specific set of pixels on a screen that may lie in front of asubstrate that emits or absorbs photons. This transformation may beaccomplished by way of changing the nanoscale orientation of themolecules in a liquid crystal, for example, from nematic to cholestericor smectic phase, at a specific set of pixels. This transformation maybe accomplished by way of an electric current causing photons to beemitted from a specific set of pixels made from a plurality of lightemitting diodes arranged in a meaningful pattern. This transformationmay be accomplished by any other way used to display information, suchas a computer screen, or some other output device or way of transmittinginformation. The health care practitioner may then act on the report,such that the data in the report is transformed into an action. Theaction may be to continue or discontinue the pregnancy, in which case agestating fetus is transformed into non-living fetus. Alternately, onemay transform a set of genotypic measurements into a report that helps aphysician treat his pregnant patient.

In some embodiments, the methods described herein can be used at a veryearly gestational age, for example as early as four week, as early asfive weeks, as early as six weeks, as early as seven weeks, as early aseight weeks, as early as nine weeks, as early as ten weeks, as early aseleven weeks, and as early as twelve weeks.

Any of the embodiments disclosed herein may be implemented in digitalelectronic circuitry, integrated circuitry, specially designed ASICs(application-specific integrated circuits), computer hardware, firmware,software, or in combinations thereof. Apparatus of the presentlydisclosed embodiments can be implemented in a computer program producttangibly embodied in a machine-readable storage device for execution bya programmable processor; and method steps of the presently disclosedembodiments can be performed by a programmable processor executing aprogram of instructions to perform functions of the presently disclosedembodiments by operating on input data and generating output. Thepresently disclosed embodiments can be implemented advantageously in oneor more computer programs that are executable and/or interpretable on aprogrammable system including at least one programmable processor, whichmay be special or general purpose, coupled to receive data andinstructions from, and to transmit data and instructions to, a storagesystem, at least one input device, and at least one output device. Eachcomputer program can be implemented in a high-level procedural orobject-oriented programming language or in assembly or machine languageif desired; and in any case, the language can be a compiled orinterpreted language. A computer program may be deployed in any form,including as a stand-alone program, or as a module, component,subroutine, or other unit suitable for use in a computing environment. Acomputer program may be deployed to be executed or interpreted on onecomputer or on multiple computers at one site, or distributed acrossmultiple sites and interconnected by a communication network.

Computer readable storage media, as used herein, refers to physical ortangible storage (as opposed to signals) and includes without limitationvolatile and non-volatile, removable and non-removable media implementedin any method or technology for the tangible storage of information suchas computer-readable instructions, data structures, program modules orother data. Computer readable storage media includes, but is not limitedto, RAM, ROM, EPROM, EEPROM, flash memory or other solid state memorytechnology, CD-ROM, DVD, or other optical storage, magnetic cassettes,magnetic tape, magnetic disk storage or other magnetic storage devices,or any other physical or material medium which can be used to tangiblystore the desired information or data or instructions and which can beaccessed by a computer or processor.

Targeted Enrichment and Sequencing

The use of a technique to enrich a sample of DNA at a set of target locifollowed by sequencing as part of a method for non-invasive prenatalallele calling or ploidy calling may confer a number of unexpectedadvantages. In some embodiments of the present disclosure, the methodinvolves measuring genetic data for use with an informatics basedmethod, such as PARENTAL SUPPORT™ (PS). The ultimate outcome of some ofthe embodiments is the actionable genetic data of an embryo or a fetus.There are many methods that may be used to measure the genetic data ofthe individual and/or the related individuals as part of embodiedmethods. In an embodiment, a method for enriching the concentration of aset of targeted alleles is disclosed herein, the method comprising oneor more of the following steps: targeted amplification of geneticmaterial, addition of loci specific oligonucleotide probes, ligation ofspecified DNA strands, isolation of sets of desired DNA, removal ofunwanted components of a reaction, detection of certain sequences of DNAby hybridization, and detection of the sequence of one or a plurality ofstrands of DNA by DNA sequencing methods. In some cases the DNA strandsmay refer to target genetic material, in some cases they may refer toprimers, in some cases they may refer to synthesized sequences, orcombinations thereof. These steps may be carried out in a number ofdifferent orders. Given the highly variable nature of molecular biology,it is generally not obvious which methods, and which combinations ofsteps, will perform poorly, well, or best in various situations.

For example, a universal amplification step of the DNA prior to targetedamplification may confer several advantages, such as removing the riskof bottlenecking and reducing allelic bias. The DNA may be mixed anoligonucleotide probe that can hybridize with two neighboring regions ofthe target sequence, one on either side. After hybridization, the endsof the probe may be connected by adding a polymerase, a means forligation, and any necessary reagents to allow the circularization of theprobe. After circularization, an exonuclease may be added to digest tonon-circularized genetic material, followed by detection of thecircularized probe. The DNA may be mixed with PCR primers that canhybridize with two neighboring regions of the target sequence, one oneither side. After hybridization, the ends of the probe may be connectedby adding a polymerase, a means for ligation, and any necessary reagentsto complete PCR amplification. Amplified or unamplified DNA may betargeted by hybrid capture probes that target a set of loci; afterhybridization, the probe may be localized and separated from the mixtureto provide a mixture of DNA that is enriched in target sequences.

In some embodiments the detection of the target genetic material may bedone in a multiplexed fashion. The number of genetic target sequencesthat may be run in parallel can range from one to ten, ten to onehundred, one hundred to one thousand, one thousand to ten thousand, tenthousand to one hundred thousand, one hundred thousand to one million,or one million to ten million. Note that the prior art includesdisclosures of successful multiplexed PCR reactions involving pools ofup to about 50 or 100 primers, and not more. Prior attempts to multiplexmore than 100 primers per pool have resulted in significant problemswith unwanted side reactions such as primer-dimer formation.

In some embodiments, this method may be used to genotype a single cell,a small number of cells, two to five cells, six to ten cells, ten totwenty cells, twenty to fifty cell, fifty to one hundred cells, onehundred to one thousand cells, or a small amount of extracellular DNA,for example from one to ten picograms, from ten to one hundredpicograms, from one hundred picograms to one nanogram, from one to tennanograms, from ten to one hundred nanograms, or from one hundrednanograms to one microgram.

The use of a method to target certain loci followed by sequencing aspart of a method for allele calling or ploidy calling may confer anumber of unexpected advantages. Some methods by which DNA may betargeted, or preferentially enriched, include using circularizingprobes, linked inverted probes (LIPs, MIPs), capture by hybridizationmethods such as SURESELECT, and targeted PCR or ligation-mediated PCRamplification strategies.

In some embodiments, a method of the present disclosure involvesmeasuring genetic data for use with an informatics based method, such asPARENTAL SUPPORT™ (PS). PARENTAL SUPPORT™ is an informatics basedapproach to manipulating genetic data, aspects of which are describedherein. The ultimate outcome of some of the embodiments is theactionable genetic data of an embryo or a fetus followed by a clinicaldecision based on the actionable data. The algorithms behind the PSmethod take the measured genetic data of the target individual, often anembryo or fetus, and the measured genetic data from related individuals,and are able to increase the accuracy with which the genetic state ofthe target individual is known. In an embodiment, the measured geneticdata is used in the context of making paternity determinations duringprenatal genetic diagnosis. There are many methods that may be used tomeasure the genetic data of the individual and/or the relatedindividuals in the aforementioned contexts. The different methodscomprise a number of steps, those steps often involving amplification ofgenetic material, addition of oligonucleotide probes, ligation ofspecified DNA strands, isolation of sets of desired DNA, removal ofunwanted components of a reaction, detection of certain sequences of DNAby hybridization, detection of the sequence of one or a plurality ofstrands of DNA by DNA sequencing methods. In some cases the DNA strandsmay refer to target genetic material, in some cases they may refer toprimers, in some cases they may refer to synthesized sequences, orcombinations thereof. These steps may be carried out in a number ofdifferent orders. Given the highly variable nature of molecular biology,it is generally not obvious which methods, and which combinations ofsteps, will perform poorly, well, or best in various situations.

Some embodiments of the present disclosure involve the use of “LinkedInverted Probes” (LIPs), which have been previously described in theliterature. LIPs is a generic term meant to encompass technologies thatinvolve the creation of a circular molecule of DNA, where the probes aredesigned to hybridize to targeted region of DNA on either side of atargeted allele, such that addition of appropriate polymerases and/orligases, and the appropriate conditions, buffers and other reagents,will complete the complementary, inverted region of DNA across thetargeted allele to create a circular loop of DNA that captures theinformation found in the targeted allele. LIPs may also be calledpre-circularized probes, pre-circularizing probes, or circularizingprobes. The LIPs probe may be a linear DNA molecule between 50 and 500nucleotides in length, and in an embodiment between 70 and 100nucleotides in length; in some embodiments, it may be longer or shorterthan described herein. Others embodiments of the present disclosureinvolve different incarnations, of the LIPs technology, such as PadlockProbes and Molecular Inversion Probes (MIPs).

One method to target specific locations for sequencing is to synthesizeprobes in which the 3′ and 5′ ends of the probes anneal to target DNA atlocations adjacent to and on either side of the targeted region, in aninverted manner, such that the addition of DNA polymerase and DNA ligaseresults in extension from the 3′ end, adding bases to single strandedprobe that are complementary to the target molecule (gap-fill), followedby ligation of the new 3′ end to the 5′ end of the original proberesulting in a circular DNA molecule that can be subsequently isolatedfrom background DNA. The probe ends are designed to flank the targetedregion of interest. One aspect of this approach is commonly called MIPSand has been used in conjunction with array technologies to determinethe nature of the sequence filled in.

Ligation-mediated PCR is method of PCR used to preferentially enrich asample of DNA by amplifying one or a plurality of loci in a mixture ofDNA, the method comprising: obtaining a set of primer pairs, where eachprimer in the pair contains a target specific sequence and a non-targetsequence, where the target specific sequence is designed to anneal to atarget region, one upstream and one downstream from the polymorphicsite; polymerization of the DNA from the 3-prime end of upstream primerto the fill the single strand region between it and the 5-prime end ofthe downstream primer with nucleotides complementary to the targetmolecule; ligation of the last polymerized base of the upstream primerto the adjacent 5-prime base of the downstream primer; and amplificationof only polymerized and ligated molecules using the non-target sequencescontained at the 5-prime end of the upstream primer and the 3-prime endof the downstream primer. Pairs of primers to distinct targets may bemixed in the same reaction. The non-target sequences serve as universalsequences such that all pairs of primers that have been successfullypolymerized and ligated may be amplified with a single pair ofamplification primers.

In an embodiment, a sample of DNA may be preferentially enriched using acapture by hybridization approach. Some examples of commercial captureby hybridization technologies include AGILENT's SURESELECT andILLUMINA's TRUSEQ. In capture by hybridization, a set ofoligonucleotides that is complimentary or mostly complimentary to thedesired targeted sequences is allowed to hybridize to a mixture of DNA,and then physically separated from the mixture. Once the desiredsequences have hybridized to the targeting oligonucleotides, the effectof physically removing the targeting oligonucleotides is to also removethe targeted sequences. Once the hybridized oligos are removed, they canbe heated to above their melting temperature and they can be amplified.Some ways to physically remove the targeting oligonucleotides is bycovalently bonding the targeting oligos to a solid support, for examplea magnetic bead, or a chip. Another way to physically remove thetargeting oligonucleotides is by covalently bonding them to a molecularmoiety with a strong affinity for another molecular moiety. An exampleof such a molecular pair is biotin and streptavidin, such as is used inSURESELECT. Thus that targeted sequences could be covalently attached toa biotin molecule, and after hybridization, a solid support withstreptavidin affixed can be used to pull down the biotinylatedoligonucleotides, to which are hybridized to the targeted sequences.

In some embodiments, PCR can be used to target specific locations of thegenome. In plasma samples, the original DNA is highly fragmented(typically less than 500 bp, with an average length less than 200 bp).In PCR, both forward and reverse primers must anneal to the samefragment to enable amplification. Therefore, if the fragments are short,the PCR assays must amplify relatively short regions as well. PCR assaycan be generated in large numbers, however, the interactions betweendifferent PCR assays makes it difficult to multiplex them beyond aboutone hundred assays. Various complex molecular approaches can be used toincrease the level of multiplexing, but it may still be limited to fewerthan 100, perhaps 200, or possibly 500 assays per reaction. Samples withlarge quantities of DNA can be split among multiple sub-reactions andthen recombined before sequencing. For samples where either the overallsample or some subpopulation of DNA molecules is limited, splitting thesample would introduce statistical noise. In an embodiment, a small orlimited quantity of DNA may refer to an amount below 10 pg, between 10and 100 pg, between 100 pg and 1 ng, between 1 and 10 ng, or between 10and 100 ng. Note that while this method is particularly useful on smallamounts of DNA where other methods that involve splitting into multiplepools can cause significant problems related to introduced stochasticnoise, this method still provides the benefit of minimizing bias when itis run on samples of any quantity of DNA. In these situations auniversal pre-amplification step may be used to increase the overallsample quantity. Ideally, this pre-amplification step should notappreciably alter the allelic distributions.

In general, to perform targeted sequencing of multiple (n) targets of asample (greater than 50, greater than 100, greater than 500, or greaterthan 1,000), one can split the sample into a number of parallelreactions that amplify one or a smaller number of individual targets.This has been performed in PCR multiwell plates or can be done incommercial platforms such as the FLUIDIGM ACCESS ARRAY (48 reactions persample in microfluidic chips) or DROPLET PCR by RAIN DANCE TECHNOLOGY(100s to a few thousands of targets). Unfortunately, thesesplit-and-pool methods are problematic for samples with a limited amountof DNA, as there is often not enough copies of the genome to ensure thatthere is one copy of each region of the genome in each well. This is anespecially severe problem when polymorphic loci are targeted, and therelative proportions of the alleles at the polymorphic loci are needed,as the stochastic noise introduced by the splitting and pooling willcause very poorly accurate measurements of the proportions of thealleles that were present in the original sample of DNA. Described hereis a method to effectively and efficiently amplify many PCR reactionsthat is applicable to cases where only a limited amount of DNA isavailable. In an embodiment, the method may be applied for analysis ofsingle cells, body fluids, mixtures of DNA such as the free floating DNAfound in maternal plasma, biopsies, environmental and/or forensicsamples.

In an embodiment, the targeted sequencing may involve one, a plurality,or all of the following steps. a) Generate and universally amplify alibrary with adaptor sequences on both ends of DNA fragments. b) Divideinto multiple reactions after library amplification. c) Perform about100-plex, about 1000-plex, or about 10,000-plex amplification ofselected targets using one target specific “Forward” primer per targetand one tag specific primer. d) Perform a second amplification from thisproduct using “Reverse” target specific primers and one (or more) primerspecific to a universal tag that was introduced as part of the targetspecific forward primers in the first round. e) Divide the product intomultiple aliquots and amplify subpools of targets in individualreactions (for example, 50 to 500-plex, though this can be used all theway down to singleplex. f) Pool products of parallel subpools reactions.During these amplifications primers may carry sequencing compatible tags(partial or full length) such that the products can be sequenced.

In an embodiment, it is possible to mitigate potential losses insubsequent steps by amplifying all or a fraction of the original cellfree DNA (cfDNA) sample. Various methods are available to amplify all ofthe genetic material in a sample, increasing the amount available fordownstream procedures. In an embodiment, ligation mediated PCR (LM-PCR)DNA fragments are amplified by PCR after ligation of either one distinctadaptors, two distinct adapters, or many distinct adaptors. In anembodiment, multiple displacement amplification (MDA) phi-29 polymeraseis used to amplify all DNA isothermally. In DOP-PCR and variations,random priming is used to amplify the original material DNA. Each methodhas certain characteristics such as uniformity of amplification acrossall represented regions of the genome, efficiency of capture andamplification of original DNA, and amplification performance as afunction of the length of the fragment.

Traditional PCR assay design results in significant losses of distinctfetal molecules, but losses can be greatly reduced by designing veryshort PCR assays, termed mini-PCR assays. Fetal cfDNA in maternal serumis highly fragmented and the fragment sizes are distributed inapproximately a Gaussian fashion with a mean of about 160 bp, a standarddeviation of about 15 bp, a minimum size of about 100 bp, and a maximumsize of about 220 bp. The distribution of fragment start and endpositions with respect to the targeted polymorphisms, while notnecessarily random, vary widely among individual targets and among alltargets collectively and the polymorphic site of one particular targetlocus may occupy any position from the start to the end among thevarious fragments originating from that locus. Note that the termmini-PCR may equally well refer to normal PCR with no additionalrestrictions or limitations.

During PCR, amplification will only occur from template DNA fragmentscomprising both forward and reverse primer sites. Because fetal cfDNAfragments are short, the likelihood of both primer sites being presentthe likelihood of a fetal fragment of length L comprising both theforward and reverse primers sites is ratio of the length of the ampliconto the length of the fragment. Under ideal conditions, assays in whichthe amplicon is 45, 50, 55, 60, 65, or 70 bp will successfully amplifyfrom about 72%, 69%, 66%, 63%, 59%, or 56%, respectively, of availabletemplate fragment molecules. The amplicon length is the distance betweenthe 5-prime ends of the forward and reverse priming sites. Ampliconlength that is shorter than typically used by those known in the art mayresult in more efficient measurements of the desired polymorphic loci byonly requiring short sequence reads. In an embodiment, a substantialfraction of the amplicons should be less than 100 bp, less than 90 bp,less than 80 bp, less than 70 bp, less than 65 bp, less than 60 bp, lessthan 55 bp, less than 50 bp, or less than 45 bp.

Note that in methods known in the prior art, short assays such as thosedescribed herein are usually avoided because they are not required andthey impose considerable constraint on primer design by limiting primerlength, annealing characteristics, and the distance between the forwardand reverse primer.

Multiplex PCR may involve a single round of PCR in which all targets areamplified or it may involve one round of PCR followed by one or morerounds of nested PCR or some variant of nested PCR. Nested PCR consistsof a subsequent round or rounds of PCR amplification using one or morenew primers that bind internally, by at least one base pair, to theprimers used in a previous round. Nested PCR reduces the number ofspurious amplification targets by amplifying, in subsequent reactions,only those amplification products from the previous one that have thecorrect internal sequence. Reducing spurious amplification targetsimproves the number of useful measurements that can be obtained,especially in sequencing. Nested PCR typically entails designing primerscompletely internal to the previous primer binding sites, necessarilyincreasing the minimum DNA segment size required for amplification. Forsamples such as maternal plasma cfDNA, in which the DNA is highlyfragmented, the larger assay size reduces the number of distinct cfDNAmolecules from which a measurement can be obtained. In an embodiment, tooffset this effect, one may use a partial nesting approach where one orboth of the second round primers overlap the first binding sitesextending internally some number of bases to achieve additionalspecificity while minimally increasing in the total assay size.

In an embodiment, a multiplex pool of PCR assays are designed to amplifypotentially heterozygous SNP or other polymorphic or non-polymorphicloci on one or more chromosomes and these assays are used in a singlereaction to amplify DNA. The number of PCR assays may be between 50 and200 PCR assays, between 200 and 1,000 PCR assays, between 1,000 and5,000 PCR assays, or between 5,000 and 20,000 PCR assays (50 to200-plex, 200 to 1,000-plex, 1,000 to 5,000-plex, 5,000 to 20,000-plex,more than 20,000-plex respectively).

In an embodiment, a 100-plex to-500 plex, 500-plex to 1,000-plex,1,000-plex to 2,000-plex, 2,000-plex to 5,000-plex, 5,000-plex to10,000-plex, 10,000-plex to 20,000-plex, 20,000-plex to 50,000-plex, or50,000-plex to 100,000-plex PCR assay pool is created such that forwardand reverse primers have tails corresponding to the required forward andreverse sequences required by a high throughput sequencing instrumentsuch as the HISEQ, GAIIX, or MISEQ available from ILLUMINA. In addition,included 5-prime to the sequencing tails is an additional sequence thatcan be used as a priming site in a subsequent PCR to add nucleotidebarcode sequences to the amplicons, enabling multiplex sequencing ofmultiple samples in a single lane of the high throughput sequencinginstrument. In an embodiment, a 10,000-plex PCR assay pool is createdsuch that reverse primers have tails corresponding to the requiredreverse sequences required by a high throughput sequencing instrument.After amplification with the first 10,000-plex assay, a subsequent PCRamplification may be performed using a another 10,000-plex pool havingpartly nested forward primers (e.g. 6-bases nested) for all targets anda reverse primer corresponding to the reverse sequencing tail includedin the first round. This subsequent round of partly nested amplificationwith just one target specific primer and a universal primer limits therequired size of the assay, reducing sampling noise, but greatly reducesthe number of spurious amplicons. The sequencing tags can be added toappended ligation adaptors and/or as part of PCR probes, such that thetag is part of the final amplicon.

Fetal fraction affects performance of the test; it is more difficult todetermine the correct paternity on samples with a lower fetal fraction.There are a number of ways to enrich the fetal fraction of the DNA foundin maternal plasma. Fetal fraction can be increased by the previouslydescribed LM-PCR method already discussed as well as by a targetedremoval of long maternal fragments. In embodiment, the longer fragmentsare removed using size selection techniques. In an embodiment, prior tomultiplex PCR amplification of the target loci, an additional multiplexPCR reaction may be carried out to selectively remove long and largelymaternal fragments corresponding to the loci targeted in the subsequentmultiplex PCR. Additional primers are designed to anneal a site agreater distance from the polymorphism than is expected to be presentamong cell free fetal DNA fragments. These primers may be used in a onecycle multiplex PCR reaction prior to multiplex PCR of the targetpolymorphic loci. These distal primers are tagged with a molecule ormoiety that can allow selective recognition of the tagged pieces of DNA.In an embodiment, these molecules of DNA may be covalently modified witha biotin molecule that allows removal of newly formed double strandedDNA comprising these primers after one cycle of PCR. Double stranded DNAformed during that first round is likely maternal in origin. Removal ofthe hybrid material may be accomplish by the used of magneticstreptavidin beads. There are other methods of tagging that may workequally well. In an embodiment, size selection methods may be used toenrich the sample for shorter strands of DNA; for example those lessthan about 800 bp, less than about 500 bp, or less than about 300 bp.Amplification of short fragments can then proceed as usual.

In some embodiments, the target DNA may originate from single cells,from samples of DNA consisting of less than one copy of the targetgenome, from low amounts of DNA, from DNA from mixed origin (e.g.pregnancy plasma: placental and maternal DNA; cancer patient plasma andtumors: mix between healthy and cancer DNA, transplantation etc), fromother body fluids, from cell cultures, from culture supernatants, fromforensic samples of DNA, from ancient samples of DNA (e.g. insectstrapped in amber), from other samples of DNA, and combinations thereof.

In some embodiments, the methods described herein may be used to amplifyand/or detect SNPs, single tandem repeats (STRs), copy number,nucleotide methylation, mRNA levels, other types of RNA expressionlevels, other genetic and/or epigenetic features. The mini-PCR methodsdescribed herein may be used along with next-generation sequencing; itmay be used with other downstream methods such as microarrays, countingby digital PCR, real-time PCR, Mass-spectrometry analysis etc.

In some embodiment, the mini-PCR amplification methods described hereinmay be used as part of a method for accurate quantification of minoritypopulations. It may be used for absolute quantification using spikecalibrators. It may be used for mutation/minor allele quantificationthrough very deep sequencing, and may be run in a highly multiplexedfashion. It may be used for standard paternity and identity testing ofrelatives or ancestors, in human, animals, plants or other creatures. Itmay be used for forensic testing. It may be used for rapid genotypingand copy number analysis (CN), on any kind of material, e.g. amnioticfluid and CVS, sperm, product of conception (POC). It may be used forsingle cell analysis, such as genotyping on samples biopsied fromembryos. It may be used for rapid embryo analysis (within less than one,one, or two days of biopsy) by targeted sequencing using min-PCR.

Highly multiplexed PCR can often result in the production of a very highproportion of product DNA resulting from unproductive side reactionssuch as primer dimer formation. In an embodiment, the particular primersthat are most likely to cause unproductive side reactions may be removedfrom the primer library to give a primer library that will result in agreater proportion of amplified DNA that maps to the genome. The step ofremoving problematic primers, that is, those primers that areparticularly likely to firm dimers has unexpectedly enabled extremelyhigh PCR multiplexing levels for subsequent analysis by sequencing. Insystems such as sequencing, where performance significantly degrades byprimer dimers and/or other mischief products, greater than 10, greaterthan 50, and greater than 100 times higher multiplexing than otherdescribed multiplexing has been achieved. Note this is opposed to probebased detection methods, e.g. microarrays, TaqMan, PCR etc. where anexcess of primer dimers will not affect the outcome appreciably. Alsonote that the general belief in the art is that multiplexing PCR forsequencing is limited to about 100 assays in the same well.

There are a number of ways to choose primers for a library where theamount of non-mapping primer-dimer or other primer mischief products areminimized. Empirical data indicate that a small number of ‘bad’ primersare responsible for a large amount of non-mapping primer dimer sidereactions. Removing these ‘bad’ primers can increase the percent ofsequence reads that map to targeted loci. One way to identify the ‘bad’primers is to look at the sequencing data of DNA that was amplified bytargeted amplification; those primer dimers that are seen with greatestfrequency can be removed to give a primer library that is significantlyless likely to result in side product DNA that does not map to thegenome. There are also publicly available programs that can calculatethe binding energy of various primer combinations, and removing thosewith the highest binding energy will also give a primer library that issignificantly less likely to result in side product DNA that does notmap to the genome.

Note that there are other methods for determining which PCR probes arelikely to form dimers. In an embodiment, analysis of a pool of DNA thathas been amplified using a non-optimized set of primers may besufficient to determine problematic primers. For example, analysis maybe done using sequencing, and those dimers which are present in thegreatest number are determined to be those most likely to form dimers,and may be removed.

To select target locations, one may start with a pool of alleged primerpair designs and create a thermodynamic model of potentially adverseinteractions between primer pairs, and then use the model to eliminatedesigns that are incompatible with other the designs in the pool.

There are many workflows that are possible when conducting PCR; someworkflows typical to the methods disclosed herein are described. Thesteps outlined herein are not meant to exclude other possible steps nordoes it imply that any of the steps described herein are required forthe method to work properly. A large number of parameter variations orother modifications are known in the literature, and may be made withoutaffecting the essence of the invention. One particular generalizedworkflow is given below followed by a number of possible variants. Thevariants typically refer to possible secondary PCR reactions, forexample different types of nesting that may be done (step 3). It isimportant to note that variants may be done at different times, or indifferent orders than explicitly described herein.

1. The DNA in the sample may have ligation adapters, often referred toas library tags or ligation adaptor tags (LTs), appended, where theligation adapters contain a universal priming sequence, followed by auniversal amplification. In an embodiment, this may be done using astandard protocol designed to create sequencing libraries afterfragmentation. In an embodiment, the DNA sample can be blunt ended, andthen an A can be added at the 3′ end. A Y-adaptor with a T-overhang canbe added and ligated. In some embodiments, other sticky ends can be usedother than an A or T overhang. In some embodiments, other adaptors canbe added, for example looped ligation adaptors. In some embodiments, theadaptors may have tag designed for PCR amplification.2. Specific Target Amplification (STA): Pre-amplification of hundreds tothousands to tens of thousands and even hundreds of thousands of targetsmay be multiplexed in one reaction. STA is typically run from 10 to 30cycles, though it may be run from 5 to 40 cycles, from 2 to 50 cycles,and even from 1 to 100 cycles. Primers may be tailed, for example for asimpler workflow or to avoid sequencing of a large proportion of dimers.Note that typically, dimers of both primers carrying the same tag willnot be amplified or sequenced efficiently. In some embodiments, between1 and 10 cycles of PCR may be carried out; in some embodiments between10 and 20 cycles of PCR may be carried out; in some embodiments between20 and 30 cycles of PCR may be carried out; in some embodiments between30 and 40 cycles of PCR may be carried out; in some embodiments morethan 40 cycles of PCR may be carried out. The amplification may be alinear amplification. The number of PCR cycles may be optimized toresult in an optimal depth of read (DOR) profile. Different DOR profilesmay be desirable for different purposes. In some embodiments, a moreeven distribution of reads between all assays is desirable; if the DORis too small for some assays, the stochastic noise can be too high forthe data to be too useful, while if the depth of read is too high, themarginal usefulness of each additional read is relatively small.

Primer tails may improve the detection of fragmented DNA fromuniversally tagged libraries. If the library tag and the primer-tailscontain a homologous sequence, hybridization can be improved (forexample, melting temperature (T_(M)) is lowered) and primers can beextended if only a portion of the primer target sequence is in thesample DNA fragment. In some embodiments, 13 or more target specificbase pairs may be used. In some embodiments, 10 to 12 target specificbase pairs may be used. In some embodiments, 8 to 9 target specific basepairs may be used. In some embodiments, 6 to 7 target specific basepairs may be used. In some embodiments, STA may be performed onpre-amplified DNA, e.g. MDA, RCA, other whole genome amplifications, oradaptor-mediated universal PCR. In some embodiments, STA may beperformed on samples that are enriched or depleted of certain sequencesand populations, e.g. by size selection, target capture, directeddegradation.

3. In some embodiments, it is possible to perform secondary multiplexPCRs or primer extension reactions to increase specificity and reduceundesirable products. For example, full nesting, semi-nesting,hemi-nesting, and/or subdividing into parallel reactions of smallerassay pools are all techniques that may be used to increase specificity.Experiments have shown that splitting a sample into three 400-plexreactions resulted in product DNA with greater specificity than one1,200-plex reaction with exactly the same primers. Similarly,experiments have shown that splitting a sample into four 2,400-plexreactions resulted in product DNA with greater specificity than one9,600-plex reaction with exactly the same primers. In an embodiment, itis possible to use target-specific and tag specific primers of the sameand opposing directionality.4. In some embodiments, it is possible to amplify a DNA sample(dilution, purified or otherwise) produced by an STA reaction usingtag-specific primers and “universal amplification”, i.e. to amplify manyor all pre-amplified and tagged targets. Primers may contain additionalfunctional sequences, e.g. barcodes, or a full adaptor sequencenecessary for sequencing on a high throughput sequencing platform.

These methods may be used for analysis of any sample of DNA, and areespecially useful when the sample of DNA is particularly small, or whenit is a sample of DNA where the DNA originates from more than oneindividual, such as in the case of maternal plasma. These methods may beused on DNA samples such as a single or small number of cells, genomicDNA, plasma DNA, amplified plasma libraries, amplified apoptoticsupernatant libraries, or other samples of mixed DNA. In an embodiment,these methods may be used in the case where cells of different geneticconstitution may be present in a single individual, such as with canceror transplants.

In some embodiments, the multiplex PCR amplification may involve usingvarious types of nesting protocol, for example: semi-nested mini-PCR,fully nested mini-PCR, heminested mini-PCR, triply hemi-nested mini-PCR,one-sided nested mini-PCR, one-sided mini-PCR or reverse semi-nestedmini-PCR.

Diagnostic Box

In an embodiment, the present disclosure comprises a diagnostic box thatis capable of partly or completely carrying out aspects of the methodsdescribed in this disclosure. In an embodiment, the diagnostic box maybe located at a physician's office, a hospital laboratory, or anysuitable location reasonably proximal to the point of patient care. Thebox may be able to run the aspects of the method in a wholly automatedfashion, or the box may require one or a number of steps to be completedmanually by a technician. In an embodiment, the box may be able toanalyze the genotypic data measured on the maternal plasma. In anembodiment, the box may be linked to means to transmit the genotypicdata measured using the diagnostic box to an external computationfacility which may then analyze the genotypic data, and possibly alsogenerate a report. The diagnostic box may include a robotic unit that iscapable of transferring aqueous or liquid samples from one container toanother. It may comprise a number of reagents, both solid and liquid. Itmay comprise a high throughput sequencer. It may comprise a computer.

Primer Kit

In some embodiments, a kit may be formulated that comprises a pluralityof primers designed to achieve the methods described in this disclosure.The primers may be outer forward and reverse primers, inner forward andreverse primers as disclosed herein; they could be primers that havebeen designed to have low binding affinity to other primers in the kitas disclosed in the section on primer design; they could be hybridcapture probes or pre-circularized probes as described in the relevantsections, or some combination thereof. In an embodiment, a kit may beformulated for determining a ploidy status of a target chromosome in agestating fetus designed to be used with the methods disclosed herein,the kit comprising a plurality of inner forward primers and optionallythe plurality of inner reverse primers, and optionally outer forwardprimers and outer reverse primers, where each of the primers is designedto hybridize to the region of DNA immediately upstream and/or downstreamfrom one of the polymorphic sites on the target chromosome, andoptionally additional chromosomes. In an embodiment, the primer kit maybe used in combination with the diagnostic box described elsewhere inthis document.

Maximum Likelihood Estimates

Many methods known in the art for detecting the presence or absence of aphenotype or genotype, for example, a chromosomal abnormality, a medicalcondition or a paternity relationship involve the use of a singlehypothesis rejection test, where a metric that is directly ralted to orcorrelated with the condition is measured, and if the metric is on oneside of a given threshold, the condition is determined to be present,while if the metric falls on the other side of the threshold, thecondition is determined to be absent. A single-hypothesis rejection testonly looks at the null distribution when deciding between the null andalternate hypotheses. Without taking into account the alternatedistribution, one cannot estimate the likelihood of each hypothesisgiven the observed data and therefore cannot calculate a confidence onthe call. Hence with a single-hypothesis rejection test, one gets a yesor no answer without an estimate of the confidence associated with thespecific case.

In some embodiments, the method disclosed herein is able to detect thepresence or absence of phenotype or genotype, for example, a chromosomalabnormality, a medical condition or a paternity relationship, using amaximum likelihood method. This is a substantial improvement over amethod using a single hypothesis rejection technique as the thresholdfor calling absence or presence of the condition can be adjusted asappropriate for each case. This is particularly relevant for diagnostictechniques that aim to determine the paternity of a gestating fetus fromgenetic data available from the mixture of fetal and maternal DNApresent in the free floating DNA found in maternal plasma. The maximumlikelihood estimation method may use the allelic distributionsassociated with each hypothesis to estimate the likelihood of the dataconditioned on each hypothesis. These conditional probabilities can thenbe converted to a hypothesis call and confidence. Similarly, maximum aposteriori estimation method uses the same conditional probabilities asthe maximum likelihood estimate, but also incorporates population priorswhen choosing the best hypothesis and determining confidence.

Therefore, the use of a maximum likelihood estimate (MLE) technique, orthe closely related maximum a posteriori (MAP) technique give twoadvantages, first it increases the chance of a correct call, and it alsoallows a confidence to be calculated for each call. In an embodiment,selecting the paternity call corresponding to the hypothesis with thegreatest probability is carried out using maximum likelihood estimatesor maximum a posteriori estimates. In an embodiment, a method isdisclosed for determining the paternity of a gestating fetus thatinvolves taking any method currently known in the art that uses a singlehypothesis rejection technique and reformulating it such that it uses aMLE or MAP technique

A Method for Paternity Determination

The ffDNA is typically present at low fraction in a mixture withmaternal DNA. In one embodiments, the mother has known genotype or thematernal genotype can be measured or inferred. Typically, the fractionof fetal DNA found in maternal plasma is between 2 and 20%, although indifferent conditions this percentage can range from about 0.01% to about50%. In an embodiment, a microarray or other technique that givesintensity data on a per allele basis can be used to measure the maternalplasma. In an embodiment, sequencing can be used to measure the DNAcontained in the maternal plasma. In these cases the allele intensitymeasurement or sequence read count at a particular allele is a sum ofthe maternal and fetal signals. Assuming that the mixture ratio of childto mother DNA is r to 1, the relative number of alleles at a locusconsists of 2 alleles from the mother and 2r alleles from the child. Insome embodiment, the loci comprise single nucleotide polymorphisms.Table 1 shows the relative number of each allele in the mixture for aselection of informative parent contexts.

TABLE 1 Number of alleles by context parent context A in mixture B inmixture AA|AA 2 + 2r 0 AA|BB 2 + r r AB|AA 1 + 2r 1 AA|AB 2 + 2r or 2 +r 0 or r BB|AA r 2 + r BB|BB 0 2 + 2r

Note that the choice of the above four contexts as being informative isnot meant to be inclusive of all contexts that may be informative. Anycombination of contexts may be used, and there is a significant amountof information that may be found in the genoypic measurements of anycontext.

Even in the presence of significant allele dropout rate from the child,there may be a clear distinction between signal where an allele ispresent and signal where an allele is not present. For example, considerthe A allele measurements from SNPs in context pairs BB|BB and BB|AA andthe B allele measurements from SNPs in from context pairs AA|AA andAA|BB. In each case, there should be no signal present in the firstcontext and there should be signal present in the second context,wherever the child's alleles have not dropped out. However, if thealleged father is incorrect, there will sometimes be signal present inboth contexts. Thus, the distribution of SNP measurements should bedifferent, depending on whether the alleged father is correct or not.

The difference will typically be more observable at the high-signal endof the distribution, because these will be the SNPs where there ishigher likelihood of having DNA contributions from the child. Thisdifference can be observed by comparing high percentile values of thedistributions of SNP measurements. Examples of possible percentilemethods are nearest rank, linear interpolation between closest ranks,and weighted percentile.

For example, define X₁ as the set of A allele SNP measurements incontext BB|BB and X₂ as the set of A allele measurements in contextBB|AA, from all chromosomes. If the alleged father is correct, then the99^(th) percentile value of X₁ will be significantly less than the99^(th) percentile value of X₂. If the alleged father is incorrect, the99^(th) percentile values of the two distributions will be closertogether. Note than any percentile may be used equally well, forexample, 95^(th) percentile, 90^(th) percentile, 85^(th) percentile or80^(th) percentile. In an embodiment, for a particular measurementchannel, X1 can be defined as the measurements from the context with nosignal and X2 can be defined as the measurements from the context wherethe mother and father are both homozygous, and only the father allelesprovide a signal (inhereted through the child).

Define p₁ as the 99th (or 95^(th), 90^(th) etc.) percentile of the X₁data and p₂ as the 99^(th) (or 95^(th), 90^(th) etc.) percentile of theX₂ data. Define the test statistic t as p₁/p₂. Note that other functionsof p1 and p2 that demonstrate the difference in values may be usedequally well. The value oft will vary depending on the amount of childDNA present in the sample, which is not known. Therefore, classificationthresholds for t can not be calculated a priori.

The test statistic t for a single sample can be compared to adistribution generated from the genotypes of many individuals who areknown not to be the father, using the following procedure. Assume thatthe genotypes from a large set of unrelated individuals are available.

-   -   1. For each unrelated individual, assume that it is the father        and calculate the value of the test statistic t.    -   2. Let T_(u) be the set of t measurements from the unrelated        males. Fit a distribution to T_(u). This is the distribution oft        for the particular sample, under the null hypothesis. The null        hypothesis is “genotypes do not come from father of child        present in sample”. The distribution Pu(t) could be a maximum        likelihood fit or method of moments fit to a known distribution        e.g. a Gaussian distribution, a kernal density fit using a        kernel function e.g. Gaussian, box, triangle etc, or any other        appropriate distribution fitting method.    -   3. Consider the genotypes of the alleged father and calculate        the corresponding test statistic t_(c).    -   4. The true father is expected to result in a smaller value oft        than an unrelated individual. The probability of an unrelated        father producing t_(c) or a more outlying value is the        cumulative density function of P_(u) evaluated at t_(c). Thus,        the p-value p for rejecting the null hypothesis is given by the        following:

p = ∫₀^(t_(c))P_(u)(t)dt

If p falls below a significance threshold α then the hypothesis that thefather alleged is an unrelated individual can be rejected withsignificance α. If p is greater than α then the null hypothesis cannotbe rejected, and the alleged father may be unrelated to the childpresent in the sample. The significance threshold α defines theprobability that an unrelated individual could be classified as thecorrect father. For example, with a threshold of α equal to 0.01, onepercent of unrelated individuals could be identified as the correctfather.

Various methods can be considered for combination of data from the A andB allele channels. For example, two simple methods are to require thatthe p-value from all channels be below a threshold, or to require thatthe p-value from any channel be below the threshold.

In some embodiments, the paternity testing method assumes that child DNAis present at sufficient concentration to distinguish between SNPs thathave or do not have signal from the child. In the absence of sufficientchild DNA concentration, this method may report “incorrect father”because expected paternally inherited alleles are not measured in thematernal plasma. In an embodiment, a method is described that canconfirm the presence of sufficient child DNA before applying thepaternity test. The child presence confirmation is based on calculationof a test statistic that is proportional to the child DNA concentration,but does not require father genotypes. If the test statistic is abovethe required threshold, then the concentration of child DNA issufficient to perform the paternity test.

Consider the set of SNPs (from all chromosomes combined) where themother genotype is AA and the B channel is measured. A signal isexpected only on the subset of SNPs where the child genotype contains aB, but these SNPs cannot be identified a priori without the fathergenotypes, which are not available. Instead, consider the SNPpopulations frequencies {f_(i)} where f_(i) is the sample mean number ofBs in the genotype of SNP i, based on a large sample population. Notethat most SNPs where the mother genotype is AA will have f_(i) less than0.5, but the distribution of f_(i) on these SNPs extends almost to one.Consider two sets of SNPs, S₁ and S₂, where S₁={i: f_(i)<T_(L)} andS2={i: f_(i)>T_(H)}. The thresholds T_(L) and T_(H) are set so that veryfew SNPs in S1 are expected to have a B and many SNPs in S2 are expectedto have a B, and each set has sufficient population. In one embodiment,the algorithm uses T_(L)=0.05 and T_(H)=0.7, while other values for TLand TH might work equally well or better. Let y_(i) be the B channelmeasurement from SNP i, Y₁={y_(i): iϵS₁}, and Y₂={y_(i): iϵS₂}. Thedistributions of Y₁ and Y₂ will be very similar because most SNPs inboth distributions will have no signal. However, some non-trivial numberof SNPs in S₂ are expected to have child signal and very few SNPs in S₁are expected to have child signal. Therefore, the tail of Y₂ shouldextend to higher intensity than the tail of Y₁. Let p_(t) be apercentile close to 1, for example, the 99th percentile. In the presenceof sufficient child DNA, the p_(t) percentile of Y₂ should besignificantly higher than the p_(t) percentile of Y₁. Thus, the teststatistic s can be defined as follows.s=percentile(Y ₂ ;p _(t))−percentile(Y ₁ ;p _(t))

In one embodiment, the test statistic may be normalized by a variety ofmethods to attempt to account for amplification differences betweenarrays. In one embodiment, the normalization could be done on a perchromosome basis. In one embodiment, the normalization could be done ona per array basis. In one embodiment, the normalization could be done ona per sequencing run basis.

The following calculation shows how the thresholds T_(L) and T_(H) areable to distinguish the effect of child DNA in particular maternalsample, based on approximate numbers of SNPs and dropout rates. Table 3shows some data from

In one embodiment, the method involves the following assumptions:

-   -   Population frequencies are calculated from a large population        data set, for example, more than 500 individuals, more than        1,000 individuals, more than 5,000 individuals or more than        20,000 individuals, and the number of SNPs in each context comes        from an example mother and father.    -   There are no SNPs where mother is AA and father is BB (in        reality, these are approximately 8 percent of mother AA SNPs)    -   Half of SNPs where father has B result in child B.    -   Child dropout rate is 90 percent.    -   Measurements with child signal will be higher than measurements        without child signal

Table 3 shows some data from a particular paternity case using thedisclosed method with the above parameters. The 98th percentilemeasurement from S₁ is not expected to include any SNPs with childsignal present. The 98th percentile measurement from S2 is expected toinclude about 50 SNPs with child signal present. The difference betweenthe two should reflect the amount of child signal.

TABLE 3 Data pertaining to paternity determination num average num numfraction SNPs f_(i) SNPs SNPs of set, set definition in set in setfather B child signal child signal S₁ f_(i) < 0.05 13300 0.012 171 90.0007 S₂ f_(i) > 0.7 3000 0.79 2370 119 0.039

FIG. 1 shows the distribution of allele intensity data for contextsAA|AA and AA|BB from a maternal plasma sample collected at 38 weeks. TheB allele is measured. Note that the AA|BB distribution extendssignificantly higher than the AA|AA distribution, showing that the Ballele (which is only present in the child's genome) is present in theAA|BB context but not the AA|AA context. FIG. 2 comes from the samematernal plasma sample as FIG. 1, and shows the distribution of the teststatistic t for allele B using the genotypes from 200 unrelatedindividuals. Two distributions are shown (the two curves): the maximumlikelihood Gaussian fit and a kernel distribution. The value t_(c) forthe biological father is marked with a star. The p-value is less than10⁻⁷ for the null hypothesis that the alleged father is unrelated to thechild.

Table 4 presents results from 8 maternal blood samples at varying stagesof pregnancy. A p-value is calculated based on the data measured fromeach channel (A allele and B allele) for the correct father. If bothchannel p-values are required to be below 0.01, then two samples areclassified incorrectly. If only one channel is required to pass thethreshold, then all samples are correctly classified. Any number ofmetrics and thresholds may be used for confirming or excludingparentage. For example, one could use a cut off p-value of 0.02, 0.005,0.001, or 0.00001; similarly, one could demand that one or both channelp-values are below a given threshold, or one could have two differentthresholds for the different channel p-values.

TABLE 4 P-values for two channels for eight paternity determinations.Weeks pregnancy p-value (Y) p-value (X) 11 2.3 × 10⁻⁷ <10⁻⁷ 16    0.013<10⁻⁷ 17 <10⁻⁷ <10⁻⁷ 17 <10⁻⁷     0.0002 20 <10⁻⁷ <10⁻⁷ 28    0.14    0.0048 38 <10⁻⁷ <10⁻⁷ 38 <10⁻⁷ <10⁻⁷

Table 4 shows the P-values for the null hypothesis that the correctfather is an unrelated individual. Each row corresponds to a differentmaternal blood sample, and the corresponding paternal genetic sample.Genetic measurements made on 200 unrelated males were used as a control.The curve in FIG. 3 shows the distribution of intensity ratios for 200unrelated males, and the star represents the intensity ratio for thebiological father. This data is taken from a case where the blood wasdrawn from a mother who was 11 weeks pregnant.

FIG. 4 shows the cumulative distribution frequency (cdf) curves for thecorrelation ratio between the fetal genotypic measurements and theparental genotypic measurements for three cases: (1) where both thepregnant mother and the alleged father are the biological parents of thefetus (“correct”, rightmost curve), (2) where the pregnant mother is thebiological mother of the fetus, but the alleged father is not thebiological father of the fetus (“one wrong”, middle curve) and (3) whereneither the pregnant mother nor the alleged father are the biologicalparents of the fetus (“two wrong”, leftmost curve). The cdf curves arethe correlation ratio between genotypic data of the embryo, calculatedfrom data measured on a single cell, and the genotypic data of theassumed parents when zero, one or two of the assumed parents areactually the genetic parents of the fetus. Note that the labels for“correct” and “two wrong” are reversed. FIG. 5 shows histograms for thesame three cases. Note that this histogram is made up of more than 1000cases where one or both parents are incorrect. The histogram ofcorrelation rate measured between the genotypic data of the fetus, asmeasured on a single cell, and the genotypic data of the assumed parentswhen zero, one or two of the assumed parents are actually the geneticparents of the fetus.

Thirty five paternity results are shown in FIG. 6 using the instantmethod for paternity testing. They were run on samples collected frompregnant women with gestational ages ranging from 9 to 40 weeks. The redcurve on the right represents a normalized Gaussian distribution of thepaternity testing statistic for 800 unrelated males. The distribution ofunrelated males is different for each case; a normalized distribution isused here for visualization purposes.

The blue bars represent the normalized test statistic for the correct(suspected) father. It is clear that the correct fathers are clearlyseparated from the unrelated males. Note that the normalized teststatistic crudely approximates standard deviations, therefore, “−5” onthe graph below is about 5 standard deviations from the mean. Thus allassumed correct fathers in this cohort have been confirmed as thecorrect fathers with a significance of at least 99.9999%.

In one embodiment of the invention, the knowledge of the parentalhaplotypes could be used to increase the accuracy of the test. Forexample, if the two haplotypes of the father are known for a givensegment of a chromosome, then the knowledge of which SNPs are presentfor cases where there is no drop out can be used to determine which SNPsshould be expected for those cases where there may be dropout. Forexample, imagine a set of three SNPs that are linked, that is, they arelocated close together on the same chromosome, and where the contexts ofthe mother and the alleged father are: AA|AB, AA|AB, AA|BA. Note thatwhen the genotype of a parent is phased, then AB≠BA, since the first ofthe two letters represents the alleles on the first haplotype, and thesecond letter represents the alleles on the second haplotype. Nowimagine that for those three SNPs, a significant level of the B alleleis measured for all three; in this case, the chance that the allegedfather is the correct father is low, because the two father haplotypesare A, A, B and B, B, A, while the measured fetal genotype is positivefor B at all three SNPs, and the mother could only have contributed anA. If the father genotype was not phased, it would not be possible torule out this alleged father given this set of measurements. In oneembodiment, that determination of the father haplotypes may bedetermined given the diploid genomic DNA measurements along with haploidgenetic measurements made on one or more sperm. The use of more than onesperm can allow the determination of the haplotypes with more accuracy,as well as how many cross overs may have occurred, for each of thechromosomes, along with their locations, during the meiosis that formedthe sperm. A method to accomplish this paternal phasing may be found ingreater detail in the four Rabinowitz patent applications referencedelsewhere in this document.

In an embodiment, the paternity determination is done exclusively usingSNP measurements, and no data from single tandem repeats is used. In anembodiment, the paternity determination is done exclusively using bothSNP and STR measurements. The SNP data may be measured using SNPmicroarrays, or it may be measured by sequencing. The sequencing may beuntargeted, or it may be targeted, for example by using circularizingprobes that are targeted to a set of polymorphic loci, or it may be usetargeted by using capture by hybridization techniques. In someembodiments, the genetic data may be measured by a combination ofmethods; for example, the parental genetic data may be measured on a SNPmicroarray while the DNA isolated from maternal serum may be measuredusing targeted sequencing where capture hybridization probes are used totarget the same SNPs as are found on the SNP microarray. In oneembodiment a combination of the following types of data may be used todetermine whether or not the alleged father is the biological father ofthe fetus: SNP data, STR data, crossover data, microdeletion data,insertion data, translocation data, or other genetic data.

In an embodiment, the method may comprise the generation of a reportdisclosing the established paternity of the fetus, or other targetindividual. In an embodiment, the report may be generated for thepurpose of communicating the paternity determination. In an embodiment,the report may comprise a probability that the alleged father is thebiological father of the fetus. Some examples of such a report are shownwithin; FIG. 7 is an example of a report disclosing a paternityexclusion, FIG. 8 is an example of a report disclosing a paternityinclusion and FIG. 9 is an example of a report indicating anindeterminate result. In one embodiment the report may comprise a graphcontaining a distribution of a paternity related metric for a pluralityof unrelated individuals with respect to a given fetus and mother (shownas a grey curve), and an indication of the metric for the alleged father(shown as a triangle). The distribution of unrelated males is differentfor each case; in these three reports, an actual distribution of thetest statistic for the fetus and unrelated males is used here. In anembodiment, the report may also contain an indication that the allegedfather is more likely to be part of the distribution of unrelatedindividuals (e.g. FIG. 7), and therefore the alleged father isestablished to not be the biological father of the fetus; the fact thatthe triangle is in the paternity exclusion region of the graph indicatesthat this is a paternity exclusion. In an embodiment, the report mayalso contain an indication that the alleged father is more likely to notbe part of the distribution of the paternity metric for unrelatedindividuals (e.g. FIG. 8), and the alleged father is established to bethe biological father of the fetus; the fact that the triangle is in thepaternity inclusion region of the graph indicates that this is apaternity inclusion. In an embodiment, the report may also contain anindication that the measurements are indeterminate (e.g. FIG. 9); thefact that the triangle is in the “indeterminate result” region of thegraph indicates that no conclusion was made with respect to establishingthe paternity of the fetus.

In one embodiment of the invention, the determination of whether or notthe alleged father is the biological father of the fetus is done withoutusing single tandem repeats (STRs). In one embodiment of the invention,the accuracy of the paternity determination is increased by phasing theparental genotypes. In one embodiment of the invention, the genotypes ofone or more of the parents are phased with the use of genetic materialfrom one or more individual related that parent. In one embodiment, theindividual related to the parent is the parents father, mother, sibling,son, daughter, brother, sister, aunt, uncle, twin, clone, a gamete fromthe parent, and combinations thereof.

Another Method for Paternity Determination

In an embodiment, the maternal plasma and optionally the other geneticmaterial may be measured by sequencing, for example using highthroughput sequencers such as the HISEQ or MISEQ by ILLUMINA, or the IONTORRENT by LIFE TECHNOLOGIES.

Non-invasive paternity testing can be performed on a maternal bloodsample if there is a sufficient concentration of free-floating fetalDNA. In general, the fraction of fetal DNA in most cases, the maternalplasma will be about between 2 percent to 20 percent, though it may beas low as 0.01%, or as high as 40%, partly depending on the gestationalage. It has already been demonstrated that this range of fetal fractionis sufficient for paternity testing by a single-hypothesis rejectionmethod using SNP microarrays. High throughput sequencing is a far moreprecise platform which allows mathematical modeling of the expectedmeasurement response at each SNP, for combinations of mother and childgenotypes. In an embodiment, the maternal plasma and optionally theother genetic material may be measured by sequencing, for example usinghigh throughput sequencers such as the HISEQ or MISEQ by ILLUMINA, orthe ION TORRENT by LIFE TECHNOLOGIES. Confidences on paternityinclusions or exclusions may then be calculated by using probabilityand/or estimation theories.

In an embodiment, the method for paternity testing may include thefollowing. For an alleged father, one may calculate the probability ofthe sequencing data, derived from the plasma, with respect to the twodifferent hypotheses: (1) the alleged father is the correct (biological)father (Hc) and (2) the alleged father is not the correct (biological)father (Hw). The hypothesis that has the higher likelihood or aposteriori is then chosen. In an embodiment, this approach may becombined with a platform model which relates the allele ratio in theplasma to the observed number of sequenced A and B alleles. With theplatform model available, it is possible to derive probabilisticlikelihoods of the sequenced A and B alleles for each SNP location foreach hypothesis.

One complication is that the amount of fetal fraction in the maternalplasma may vary between individuals and over time. In an embodiment, themethod may account for this variability. There are several ways toaddress this type of variability. In an embodiment, the method mayexplicitly estimate the fetal fraction; in another embodiment, themethod may put a prior on the unknown quantity and integrates over allpossible values. An embodiment uses a prior that is it as a uniformdistribution from 0 to some threshold, e.g. 40%. Any prior may work intheory. An embodiment, calculates likelihoods of various childfractions, either in continuous space or on a finite partition andintegrates or sums over the range, respectively.

Consider maternal plasma with fetal fraction, f, and a single SNP wherethe expected allele ratio present in the plasma is r (based on thematernal and fetal genotypes). In an embodiment, the expected alleleratio is defined as the expected fraction of A alleles in the combinedmaternal and fetal DNA. For maternal genotype g_(m) and child genotypeg_(c), the expected allele ratio is given by equation 1, assuming thatthe genotypes are represented as allele ratios as well.r=fg _(c)+(1−f)g _(m)  (1)

The observation at the SNP comprises the number of mapped reads witheach allele present, n_(a) and n_(b), which sum to the depth of read d.Assume that quality control measures have been applied to the mappingprobabilities such that the mappings and allele observations can beconsidered correct. A simple model for the observation likelihood is abinomial distribution which assumes that each of the d reads is drawnindependently from a large pool that has allele ratio r. Equation 2describes this model.

$\begin{matrix}{{P\left( {n_{a},\left. n_{b} \middle| r \right.} \right)} = {{p_{bino}\left( {{n_{a};{n_{a} + n_{b}}},r} \right)} = {\begin{pmatrix}{n_{a} + n_{b}} \\n_{a}\end{pmatrix}{r^{n_{a}}\left( {1 - r} \right)}^{n_{b}}}}} & (2)\end{matrix}$

When the maternal and fetal genotypes are either all A or all B, theexpected allele ratio in plasma will be 0 or 1, and P_(bino) will not bewell-defined. Additionally, this is not desirable because unexpectedalleles are sometimes observed in practice. The binomial model can beextended in a number of ways. In an embodiment, it is possible to use acorrected allele ratio {circumflex over (r)}=1/(n_(a)+n_(b)) to allow asmall amount of the unexpected allele to be accounted for. In anembodiment, it is possible to use training data to model the rate of theunexpected allele appearing on each SNP, and use this model to correctthe expected allele ratio. When the expected allele ratio is not 0 or 1,the observed allele ratio may not converge to the expected allele ratiodue to amplification bias or other phenomena. The allele ratio can thenbe modeled as a beta distribution centered at the expected allele ratio,leading to a beta-binomial distribution for P(n_(a), n_(b)|r) which hashigher variance than the binomial.

A general platform model for the response at a single SNP may be definedas F(a, b, g_(c), g_(m), f) (3), or the probability of observing n_(a)=aand n_(b)=b given the maternal and fetal genotypes, which also dependson the fetal fraction through equation 1.F(a,b,g _(c) ,g _(m) ,f)=P(n _(a) =a,n _(b) =b|g _(c) ,g _(m) ,f)  (3)

Note that it may be feasible to simplify formula (3) by conditioning ona function of g_(c), g_(m) and f e.g. by using r as defined in (1) andthe binomial example in (2). The equation for F could then be writtenF(a,b,g _(c) ,g _(m) ,f)=P(n _(a) =a,n _(b) =b|g _(c) ,g _(m) ,f)=P(n_(a) =a,n _(b) =b|r(g _(c) ,g _(m) ,f))  (4)

In general the functional form of F may be a binomial distribution,beta-binomial distribution, multivariate Pólya distribution, anempirical distribution estimated from training data, or similarfunctions as discussed above. In an embodiment, the functional form of Ftakes different forms depending on the hypothesis for copy number on thechromosome in question.

A Method for the Calculation of the Fetal Fraction

Determining the fraction of fetal DNA that is present in the mixedfraction of DNA may be an integral part of any method for non-invasiveprenatal paternity determination, ploidy calling, or allele calling. Insome embodiments, the fetal fraction of the mixed sample may bedetermined using the genotypic data of the mother, the genotypic data ofthe father, and the measured genotypic data from the mixed sample thatcontains both maternal and fetal DNA. In the context of paternitytesting, and also to a lesser extent in the case of ploidy calling, theidentity of the father is not known, and therefore genotypic data of thebiological father of a fetus may not be available. In these cases, it isimportant to have a method for fetal fraction determination that doesnot require the genotype of the biological father of the fetus.Described herein are several method by which to accomplish the fetalfraction estimate. These methods are described in a general way suchthat they are appropriate when the genotype of the biological father isavailable, and when it is not.

For a particular chromosome, suppose we are looking at N SNPs, for whichwe have the following data:

-   -   A set of NR plasma sequence measurements S=(S₁, . . . , S_(NR)).        In an embodiment, where we have (A,B) counts for alleles A and B        for each SNP, s can be written as s=((a₁, b₁), . . . , (a_(N),        b_(N))), where a_(i) is the a count on SNP i, b_(i) is the b        count on SNP i, and Σ_(i=1:N)(a_(i)+b_(i))=NR    -   Parent data consisting of:        -   Genotype information: mother G_(m)=(G_(m1), . . . , G_(mN)),            father G_(f)=(G_(f1), . . . , G_(fN)), where G_(mi),            G_(fi)∈(AA,AB,BB); and/or        -   Sequence data measurements: NRM mother measurements            s_(m)=(s_(m1), . . . , s_(mnr)), NRF father measurements            S_(f)=(S_(f1), . . . , S_(fnr)). Similar to above            simplification, if we have (A,B) counts on each SNP            S_(m)=((a_(m1), b_(m1)), . . . , (a_(mN), b_(mN))),            S_(f)=((a_(f1), b_(f1)), . . . , (a_(fN), b_(fN)))            Collectively, mother, father child data may be denoted as            D=(G_(m), G_(f), S_(m), S_(f), S). In an embodiment,            genotypic data from both parents are available; in an            embodiment, genotypic data from only the mother is            available; in an embodiment, genotypic data from only the            father is available; in an embodiment, genotypic data from            neither parent is available. In some embodiment, the            maternal genotypic data may be inferred from the genotypic            data measured in the mixed sample. Note that in general,            parent data is desirable and increases the accuracy of the            algorithm, but is not required.

Child fraction estimate f is the expected child fraction given the data:{circumflex over (f)}=E(cfr|D)=∫f*P(f|D)df

In an embodiment, one may partition the interval of possible childfractions to a set C of finely spaced points and perform thecalculations at each point which reduce the above equation to:

$\hat{f} = {{E\left( f \middle| D \right)} = {\sum\limits_{f \in C}{f*{P\left( f \middle| D \right)}}}}$P(f|D) is the likelihood of particular child fraction f given the dataD. One may further derive using Bayes rule:P(f|D)˜P(D|f)*P(f)where P(f) is the prior weight of particular child fraction. In anembodiment, this may be derived from uninformed prior (uniform) and maybe proportional to the spacing between candidate child fractions in setC.

P(D|cfr) is the likelihood of given data given the particular childfraction, derived under the particular copy number assumptions on therelevant chromosomes. In an embodiment, one may we assume disomy on thechromosomes used. Likelihood of the data on all SNPs is the product oflikelihood of data on individual SNPs.

${P\left( D \middle| f \right)} = {{P\left( {\left. D \middle| f \right.,H} \right)} = {\underset{i}{\Pi}{P\left( {\left. D \middle| f \right.,H,i} \right)}}}$Where i denotes a particular SNP, for SNP i we have:

${P\left( {\left. D \middle| f \right.,H,i} \right)} = {\sum\limits_{{\mathcal{g}}_{m},{\mathcal{g}}_{f},{\mathcal{g}}_{c}}{{P\left( {\left. D \middle| {\mathcal{g}}_{m} \right.,{\mathcal{g}}_{f},{\mathcal{g}}_{c},f,H,i} \right)}*{P\left( {\left. {\mathcal{g}}_{c} \middle| {\mathcal{g}}_{m} \right.,{\mathcal{g}}_{f},H} \right)}*{P\left( {\mathcal{g}}_{m} \middle| i \right)}*{P\left( {\mathcal{g}}_{f} \middle| i \right)}}}$where g_(m) are possible true mother genotypes, g_(f) are possible truefather genotypes, g_(c) are possible child genotypes, and g_(m), g_(f),g_(c) ∈{AA, AB, BB}.

P(g_(m)|i) is the general prior probability of mother genotype g_(m) onSNP i, based on the known population frequency at SNP i, denoted pA_(i).In particular:p(AA|pA _(i))=(pA _(i))² ,p(AB|pA _(i))=2(pA _(i))*(1−pA _(i)),p(BB|pA_(i))=(1−pA _(i))²Same for p(f|i), father genotype probability.

Let P(g_(c)|g_(m), g_(f), H) denote is the probability of getting truechild genotype=c, given parents m, f, and assuming hypothesis H, whichwe can easily calculate. For example, for a disomy:

parents P(c | m, f, disomy) m f AA AB BB AA AA 1 0 0 AB AA 0.5 0.5 0 BBAA 0 1 0 AA AB 0.5 0.5 0 AB AB 0.25 0.5 0.25 BB AB 0 0.5 0.5 AA BB 0 1 0AB BB 0 0.5 0.5 BB BB 0 0 1

Let P(D|g_(m), g_(f), g_(c), H, i, f) be the probability of given data Don SNP i, given true mother genotype m, true father genotype f, truechild genotype c, hypothesis H for the copy number and child fraction f.It can be broken down into probability of mother, father and child dataas follows:P(D|g _(m) ,g _(f) ,g _(c) ,H,f,i)=P(s _(m) |g _(m) ,i)P(G _(m) |g _(m),i)P(s _(f) |g _(f) ,i)P(G _(f) |g _(f) ,i)P(s|g _(m) ,g _(c) ,H,f,i)

The probability of mother illumina genotype data g_(mi) at SNP icompared to true genotype g_(m), assuming illumina genotypes arecorrect, is simply:

${P\left( {\left. G_{m} \middle| g_{m} \right.,i} \right)} = \left\{ \begin{matrix}1 & {g_{mi} = g_{m}} \\0 & {g_{mi} \neq g_{m}}\end{matrix} \right.$

In an embodiment, the probability of mother sequence data at SNP i, incase of counts S_(mi)=(am_(i),bm_(i)), with no extra noise or biasinvolved, is the binomial probability defined as:P(S_(m)|,i)=P_(X|m)(am_(i)) where X|m˜Binom(p_(m)(A), am_(i)+bm_(i))with p_(m)(A) defined as:

m AA AB BB A B nocall p(A) 1 0.5 0 1 0 0.5A similar equation applies for father probabilities.

Note that it is possible to get an answer without the parent data,especially without the father data. For example if no father genotypedata F is available, one can use P(G_(f)|g_(f), i)=1. If no fathersequence data S_(f) is available, one can use P(S_(f)|g_(f),i)=1. In anembodiment, information from different chromosomes is aggregated usingaverages, weighted average or a similar function.

Another Method for the Calculation of the Fetal Fraction

Another method for determining the fraction of fetal DNA in a mixture ofDNA is described here. In one embodiment, a version of a maximumlikelihood estimate of the fetal fraction f for a paternity test, ploidytest, or other purpose, may be derived without the use of paternalinformation. Define S₀ as the set of SNPs with maternal genotype 0 (AA),S_(0.5) as the set of SNPs with maternal genotype 0.5 (AB) and S₁ as theset of SNPs with maternal genotype 1 (BB). The possible fetal genotypeson S₀ are 0 and 0.5, resulting in a set of possible allele ratios

${R_{0}(f)} = {\left\{ {0,\frac{f}{2}} \right\}.}$Similarly, R_(0.5)={0.5−f, 0.5, 0.5+f} and

${R_{1}(f)} = {\left\{ {{1 - \frac{f}{2}},1} \right\}.}$All or any subset of the sets S₀, S_(0.5) and S₁ can be used to derive achild fraction estimate.

Define N_(a0) and N_(b0) as the vectors formed by sequence counts forSNPs in S₀, N_(a0.5) and N_(b0.5) similarly for S_(0.5), and N_(a1) andN_(b1) similarly for S₁. The maximum likelihood estimate {circumflexover (f)} of f, using all maternal genotype sets, is defined by equation4.{circumflex over (f)}=arg max_(f) P(N _(a0) ,N _(b0|f))P(N _(a0.5) ,N_(b0.5) |f)P(N _(a1) ,N _(b1) |f)  (4)

Assuming that the allele counts at each SNP are independent conditionedon the SNP's plasma allele ratio, the probabilities can be expressed asproducts over the SNPs in each set:P(N _(a0) ,N _(b0) |f)=Π_(s∈S) ₀ P(n _(as) ,n _(bs) |f)P(N _(a1) ,N _(b1) |f)=Π_(s∈S) ₁ P(n _(as) ,n _(bs) |f)  (5)where n_(as), n_(bs) are the counts on SNPs s.

The dependence on f is through the sets of possible allele ratios R₀(f),R_(0.5)(f) and R₁(f). The SNP probability P(n_(as), n_(bs)|f) can beapproximated by assuming the maximum likelihood genotype conditioned onf. At reasonably high fetal fraction and depth of read, the selection ofthe maximum likelihood genotype will be high confidence. For example, atfetal fraction of 10 percent and depth of read of 1,000, consider a SNPwhere the mother has genotype 0. The expected allele ratios are 0 and 5percent, which will be easily distinguishable at sufficiently high depthof read. Substitution of the estimated child genotype into equation 5results in the complete equation (6) for the fetal fraction estimate.

$\hat{f} = {\arg\mspace{14mu}{\max_{f}\begin{bmatrix}{{\Pi_{s \in S_{0}}\left( {\max\limits_{r_{s} \in {R_{0}{(f)}}}{P\left( {n_{as},\left. n_{bs} \middle| r_{s} \right.} \right)}} \right)}\mspace{14mu}{\Pi_{s \in S_{0.5}}\left( {\max\limits_{r_{s} \in {R_{0.5}{(f)}}}{P\left( {n_{as},\left. n_{bs} \middle| r_{s} \right.} \right)}} \right)}} \\{\Pi_{s \in S_{1}}\left( {\max\limits_{r_{s} \in {R_{1}{(f)}}}{P\left( {n_{as},\left. n_{bs} \middle| r_{s} \right.} \right)}} \right)}\end{bmatrix}}}$

The fetal fraction must be in the range [0, 1] and so the optimizationcan be easily implemented by a constrained one-dimensional search.

Another method would be to sum over the possible genotypes at each SNP,resulting in the following expression (7) for P(n_(a), n_(b)|f) for aSNP in S₀. The prior probability P(r) could be assumed uniform overR₀(f), or could be based on population frequencies. The extension togroups S_(0.5) and S₁ is trivial.P(n _(a) ,n _(b) |f)=Σ_(r∈R) ₀ _((f)) P(n _(a) ,n _(b) |r)P(r)  (7)Derivation of Probabilities

A confidence can be calculated from the data likelihoods of the twohypotheses H_(tf) i.e. the alleged father is the biological father andH_(wf) i.e. the alleged father is not the biological father. Theobjective is to calculate P(H|D) i.e. probability of hypothesis givendata, for each hypothesis and infer which hypothesis is more likely. Inone embodiment, this may be done using Bayes rule: P(H|D)˜P(D|H)*P(H)where P(H) is the prior weight of the hypothesis, and where P(D|H) isthe likelihood of data given the hypothesis.

Consider P(D|H,f) i.e. the likelihood of data given hypothesis for aparticular child fraction. If a distribution on child fraction isavailable, it is possible to deriveP(D|H)=∫P(D,f|H)dfand further,P(D|H)=∫P(D|H,f)P(f|H)df

Note that P(f|H) is independent of the hypothesis i.e. P(f|H)=P(f) sincethe child fraction is the same regardless of whether the alleged fatheris the biological father or not, and any reasonable prior P(f) could bechosen e.g. a uniform prior from 0 to 50% child fraction. In anembodiment, it is possible to use only one child fraction, {circumflexover (f)}. In this case,P(D|H)=P(D|H,{circumflex over (f)})

Consider the likelihood P(D|H,f). The likelihood of each hypothesis isderived based on the response model, the estimated fetal fraction, themother genotypes, the alleged father genotypes, allele populationfrequencies, the plasma allele counts and SNPs. Let D represent the dataas defined before.

In an embodiment, it is assumed that the observation at each SNP isindependent conditioned on the plasma allele ratio, thus the likelihoodof a paternity hypothesis is the product of the likelihoods on the SNPs:

${P\left( {\left. D \middle| H \right.,f} \right)} = {\underset{SNPsi}{\Pi}{P\left( {\left. D \middle| H \right.,f,i} \right)}}$

The following equations describe how one may derive the likelihood for asingle SNP i and a single child fraction f. Equation 8 is a generalexpression for the likelihood of any hypothesis H, which will then bebroken down into the specific cases of H_(tf) and H_(wf). Note thatgenotypes, g_(m), g_(tf), g_(df), and g_(c), take values in {AA,AB,BB}which translates to {0, 0.5, 1} where AA=0, AB=0.5, BB=1. Also, g_(tf)denote the genotypes of the true father and g_(df) denote the genotypesrepresented by the data provided for the fater. In case of H_(tf),g_(tf) and g_(df) are equivalent.P(D|f,H,i)=Σ_(g) _(m) _(,g) _(tf) _(,g) _(df) _(,g) _(c) _(∈{0,0.5,1})P(D|g _(m) ,g _(df) ,g _(c) ,f,H,i)*P(g _(c) |g _(m) ,g _(tf) ,H)*P(g_(m) |i)*P(g _(tf) |i)*P(g _(df) |i)  (8)

In the case of the hypothesis H_(tf), the alleged father is thebiological father and the fetal genotypes are inherited from thematernal genotypes and alleged father genotypes. The equation abovesimplifies to:

$\begin{matrix}{{{P\left( {\left. D \middle| f \right.,{H = H_{tf}},i} \right)} = {\sum\limits_{{\mathcal{g}}_{m},{\mathcal{g}}_{tf},{{\mathcal{g}}_{c} \in {\{{0,0.5,1}\}}}}{{P\left( {\left. D \middle| {\mathcal{g}}_{m} \right.,{\mathcal{g}}_{tf},{\mathcal{g}}_{c},f,{H = H_{tf}},i} \right)}*{P\left( {\left. {\mathcal{g}}_{c} \middle| {\mathcal{g}}_{m} \right.,{\mathcal{g}}_{tf},{H = H_{tf}}} \right)}*{P\left( {\mathcal{g}}_{m} \middle| i \right)}*{P\left( {\mathcal{g}}_{tf} \middle| i \right)}}}}\mspace{76mu}{{Further},\mspace{76mu}{{P\left( {\left. {\mathcal{g}}_{c} \middle| {\mathcal{g}}_{m} \right.,{\mathcal{g}}_{tf},{H = H_{tf}}} \right)} = {P\left( {\left. {\mathcal{g}}_{c} \middle| {\mathcal{g}}_{m} \right.,{\mathcal{g}}_{tf}} \right)}}}\mspace{76mu}{and}{{P\left( {\left. D \middle| {\mathcal{g}}_{m} \right.,{\mathcal{g}}_{tf},{\mathcal{g}}_{c},f,{H = H_{tf}},i} \right)} = {{P\left( {\left. s_{m} \middle| g_{m} \right.,i} \right)}{P\left( {\left. G_{m} \middle| g_{m} \right.,i} \right)}{P\left( {\left. s_{f} \middle| g_{tf} \right.,i} \right)}{P\left( {\left. G_{f} \middle| g_{tf} \right.,i} \right)}{P\left( {\left. s \middle| g_{m} \right.,g_{c},f,i} \right)}}}} & (9)\end{matrix}$

In the case of H_(wf), the alleged father is not the biological father.One estimate of the true father genotypes may be generated using thepopulation frequencies at each SNP. Thus, the probabilities of childgenotypes may be determined by the known mother genotypes and thepopulation frequencies, i.e. the data do not provide additionalinformation on the genotypes of the biological father. In this case, theequation above does not further simplify and stays as:

$\begin{matrix}{{{P\left( {\left. D \middle| f \right.,{H = H_{wf}},i} \right)} = {\sum\limits_{{\mathcal{g}}_{m},{\mathcal{g}}_{tf},{\mathcal{g}}_{df},{{\mathcal{g}}_{c} \in {\{{0,0.5,1}\}}}}{{P\left( {\left. D \middle| {\mathcal{g}}_{m} \right.,{\mathcal{g}}_{df},{\mathcal{g}}_{c},f,{H = H_{wf}},i} \right)}*{P\left( {\left. {\mathcal{g}}_{c} \middle| {\mathcal{g}}_{m} \right.,{\mathcal{g}}_{tf},{H = H_{wf}}} \right)}*{P\left( {\mathcal{g}}_{m} \middle| i \right)}*{P\left( {\mathcal{g}}_{tf} \middle| i \right)}*{P\left( {\mathcal{g}}_{df} \middle| i \right)}}}}\mspace{79mu}{{Further},\mspace{79mu}{{P\left( {\left. {\mathcal{g}}_{c} \middle| {\mathcal{g}}_{m} \right.,{\mathcal{g}}_{tf},{H = H_{wf}}} \right)} = {P\left( {\left. {\mathcal{g}}_{c} \middle| {\mathcal{g}}_{m} \right.,{\mathcal{g}}_{tf}} \right)}}}\mspace{20mu}{{where}\mspace{14mu}{the}\mspace{14mu}{only}\mspace{14mu}{information}\mspace{14mu}{of}\mspace{14mu} g_{tf}\mspace{14mu}{are}\mspace{14mu}{the}\mspace{14mu}{population}}\mspace{14mu}\mspace{20mu}{{priors}\mspace{14mu}{and}\text{:}}{{P\left( {\left. D \middle| {\mathcal{g}}_{m} \right.,{\mathcal{g}}_{tf},{\mathcal{g}}_{c},f,{H = H_{wf}},i} \right)} = {{P\left( {\left. s_{m} \middle| g_{m} \right.,i} \right)}{P\left( {\left. G_{m} \middle| g_{m} \right.,i} \right)}{P\left( {\left. s_{f} \middle| g_{df} \right.,i} \right)}{P\left( {\left. G_{f} \middle| g_{df} \right.,i} \right)}{P\left( {\left. s \middle| g_{m} \right.,g_{c},f,i} \right)}}}} & (10)\end{matrix}$

In both expressions of the likelihoods, P(D|f,H,i), i.e. for bothhypotheses, the response model, P(s|g_(m), g_(df), g_(c), f, H) isgeneralized. Specific examples are mentioned elsewhere in the documentin discussions on general platform models. Some examples for theresponse model include the binomial distribution, beta-binomialdistribution, multivariate Pólya distribution, an empirical distributionestimated from training data, or similar functions as discussed above.

In some embodiments, the confidence C_(p) on correct paternity can becalculated from the likelihoods P(D|H_(tf)) and P(D|H_(wf)). In anembodiment this calculation may be calculated using Bayes rule asfollows:

$C_{p} = \frac{{P\left( D \middle| H_{tf} \right)}{P\left( H_{tf} \right)}}{{{P\left( D \middle| H_{tf} \right)}{P\left( H_{tf} \right)}} + {{P\left( D \middle| H_{wf} \right)}{P\left( H_{wf} \right)}}}$or written for a more specific case as a product over SNPs of the twolikelihoods:

$C_{p} = \frac{\Pi_{i}{P\left( {\left. D \middle| H_{tf} \right.,G_{ms},G_{tf},f} \right)}}{{\Pi_{s}{P\left( {n_{as},\left. n_{bs} \middle| H_{t} \right.,G_{ms},G_{tf},f} \right)}} + \mspace{11mu}{\Pi_{s}{P\left( {n_{as},\left. n_{bs} \middle| H_{f} \right.,G_{ms},G_{tf},f} \right)}}}$In another embodiment the confidence may be calculated as follows:

$C_{p} = \frac{P\left( D \middle| H_{tf} \right)}{{P\left( D \middle| H_{tf} \right)} + {P\left( D \middle| H_{wf} \right)}}$Other reasonable functions of the likelihoods are also possible.

EXPERIMENTAL SECTION Experiment 1

Twenty one pregnant women with confirmed paternity and gestational agesbetween 6 and 21 weeks were enrolled. Participants voluntarily donatedblood as part of our IRB approved research program, and were drawn fromIVF centers, OB offices, and the general population in differentlocations in the U.S. Cell free DNA (ffDNA) isolated from maternalplasma, along with DNA from the mother and alleged father, wereamplified and measured using a SNP array. An informatics methoddisclosed herein was used to exclude or include paternity for 21 correctfathers and 36,400 incorrect fathers by comparing each alleged fatheragainst a reference distribution generated from a set of over 5,000unrelated individuals. 20 out of 21 samples had sufficient fetal DNA toreturn results. Twenty of twenty (100%) of paternity inclusions werecorrect. 36,382 of 36,382 paternity exclusions were correct (100%), with18 “no calls” due to intermediate genetic similarity. There were nomiscalls.

The population was made up of couples who donated their blood forprenatal research. The women had to have singleton pregnancies, be inthe first or second trimester, and have confirmed paternity. Bloodsamples were collected from women using CELL-FREE blood tubes (STRECK)containing white blood cell preservative, and genetic samples werecollected from the father, either as a blood (EDTA) or buccal sample.Written informed consent was obtained from all participants, and thegenetic samples were collected from patients enrolled in an IRB approvedstudy.

Mother blood was centrifuged to isolate the buffy coat and the serum.The genomic DNA in the maternal and alleged paternal buffy coat and theDNA in the maternal serum were prepared for analysis and run on ILLUMINAINFINIUM CYTO12 SNP arrays using standard protocols. Briefly, serum DNAwas isolated using QIAGEN CIRCULATING NUCLEIC ACID kit and eluted in 45ul buffer according to manufacturer's instructions. Twenty microlitereluate was used in a blunt ending reaction in 1×NEB 4 buffer, 0.42 mMdNTP and 2.5 U T4 DNA Polymerase (NEW ENGLAND BIOLABS), incubated at 20C for 30 min, then 75 C for 15 min. Three microliter ligation mixture(0.5 ul 10×NEB 4, 1 ul 10 mM ATP, 1 ul T4 PNK (NEW ENGLAND BIOLABS), 0.5ul T4 DNA Ligase (NEW ENGLAND BIOLABS)) was added and samples incubatedat 16 C for 24 hours, then 75 C for 15 min. The sample was transferredto the standard ILLUMINA INFINIUM assay along with the maternal andalleged paternal genomic DNA. In short, 24 ul DNA was whole genomeamplified at 37 C for 20-24 hours followed by fragmentation andprecipitation. The precipitate was then resuspended in hybridizationbuffer, heat denatured and transferred to Cyto12 SNP arrays using aTECAN EVO. The arrays were incubated at 48 C for at least 16 hours,X-Stained (INFINIUM II CHEMISTRY) and washed in the TECAN EVO, andfinally scanned. Array intensities were extracted using BEADSTIDUO(ILLUMINA).

The disclosed informatics method generated a test statistic thatmeasured the degree of genetic similarity between the fetus and anotherindividual. This test statistic was calculated for both the allegedfather and a set of over 5,000 unrelated individuals. A singlehypothesis rejection test then determined whether the statisticcalculated for the alleged father could be excluded from thedistribution formed by the unrelated reference individuals. If thealleged father could be rejected from the unrelated set, then apaternity inclusion resulted; otherwise, paternity was excluded. For the20 samples with sufficient DNA, the paternity test was run against 20correct fathers, and for 1,820 randomly selected incorrect fathers.

A paternity inclusion was called when the p-value of the allegedfather's test statistic on the distribution of unrelated individuals wasless than 10⁻⁴. This means that, in theory, no more than one out of10,000 unrelated individuals are expected to show as much geneticsimilarity to the fetus. A “no call” was called where the p-value isbetween 10⁻⁴ and 0.02. An “insufficient fetal DNA” call was made whenthe fetal DNA made up less than 2% of the plasma DNA. The set ofunrelated individuals used to generate the expected distribution wascomposed of individuals from a wide variety of racial backgrounds, andthe paternity inclusion or exclusion determination was recalculated forsets of unrelated individuals of different races, including the raceindicated for the alleged father. The inclusion and exclusion resultswere automatically generated by the algorithm, and no human interventionwas necessary.

In conclusion, twenty one samples of maternal blood with known paternitywere tested. Twenty out of 21 samples returned results, while one hadinsufficient fetal DNA for analysis; this sample was drawn from a womanat 8 weeks gestational age. Twenty of twenty (100%) results had thecorrect paternity confirmed, each with a p-value of <10⁴. Each of the 20samples with sufficient fetal fraction was tested against a random setof 1,820 incorrect fathers, for a total of 36,400 individual paternitytests. 36,382 of these analyses returned a result; 36,382 of 36,382(100%) correctly had the paternity excluded with a p-value of greaterthan 10⁻⁴, and 18 of 36,400 (0.05%) were called “no call”, with ap-value between 10⁻⁴ and 0.02. There were no incorrect paternityexclusions or inclusions.

Nine of 21 samples had confirmed paternity due to control offertilization during IVF with correct paternity confirmed afterfertilization through pre-implantation genetic diagnosis. Twelve sampleshad paternity confirmed by independent paternity testing of fetal/childgenomic DNA, conducted by DNA Diagnostic Center, Fairfield, Ohio.

Experiment 2

In one experiment, four maternal plasma samples were prepared andamplified using a hemi-nested 9,600-plex protocol. The samples wereprepared in the following way: between 15 and 40 mL of maternal bloodwere centrifuged to isolate the buffy coat and the plasma. The genomicDNA in the maternal and was prepared from the buffy coat and paternalDNA was prepared from a blood sample or saliva sample. Cell-free DNA inthe maternal plasma was isolated using the QIAGEN CIRCULATING NUCLEICACID kit and eluted in 45 uL TE buffer according to manufacturer'sinstructions. Universal ligation adapters were appended to the end ofeach molecule of 35 uL of purified plasma DNA and libraries wereamplified for 7 cycles using adaptor specific primers. Libraries werepurified with AGENCOURT AMPURE beads and eluted in 50 ul water.

3 ul of the DNA was amplified with 15 cycles of STA (95° C. for 10 minfor initial polymerase activation, then 15 cycles of 95° C. for 30s; 72°C. for 10 s; 65° C. for 1 min; 60° C. for 8 min; 65° C. for 3 min and72° C. for 30s; and a final extension at 72° C. for 2 min) using 14.5 nMprimer concentration of 9600 target-specific tagged reverse primers andone library adaptor specific forward primer at 500 nM.

The hemi-nested PCR protocol involved a second amplification of adilution of the first STAs product for 15 cycles of STA (95° C. for 10min for initial polymerase activation, then 15 cycles of 95° C. for 30s;65° C. for 1 min; 60° C. for 5 min; 65° C. for 5 min and 72° C. for 30s;and a final extension at 72° C. for 2 min. using reverse tagconcentration of 1000 nM, and a concentration of 16.6 u nM for each of9600 target-specific forward primers.

An aliquot of the STA products was then amplified by standard PCR for 10cycles with 1 uM of tag-specific forward and barcoded reverse primers togenerate barcoded sequencing libraries. An aliquot of each library wasmixed with libraries of different barcodes and purified using a spincolumn.

In this way, 9,600 primers were used in the single-well reactions; theprimers were designed to target SNPs found on chromosomes 1, 2, 13, 18,21, X and Y. The amplicons were then sequenced using an ILLUMINA GAIIXsequencer. Per sample, approximately 3.9 million reads were generated bythe sequencer, with 3.7 million reads mapping to the genome (94%), andof those, 2.9 million reads (74%) mapped to targeted SNPs with anaverage depth of read of 344 and a median depth of read of 255. Thefetal fraction for the four samples was found to be 9.9%, 18.9%, 16.3%,and 21.2%

Relevant maternal and paternal genomic DNA samples amplified using asemi-nested 9600-plex protocol and sequenced. The semi-nested protocolis different in that it applies 9,600 outer forward primers and taggedreverse primers at 7.3 nM in the first STA. Thermocycling conditions andcomposition of the second STA, and the barcoding PCR were the same asfor the hemi-nested protocol.

The sequencing data was analyzed using informatics methods disclosedherein and each of a set of ten unrelated males from a reference setwere determined to not be the biological father of each of the gestatingfetuses.

Experiment 3

In one experiment 45 sets of cells were amplified using a 1,200-plexsemi-nested protocol, sequenced, and ploidy determinations were made atthree chromosomes. Note that this experiment is meant to simulate theconditions of performing paternity testing on single fetal cellsobtained from maternal blood, or on forensic samples where a smallamount of DNA from the child is present. 15 individual single cells and30 sets of three cells were placed in 45 individual reaction tubes for atotal of 45 reactions where each reaction contained cells from only onecell line, but the different reactions contained cells from differentcell lines. The cells were prepared into 5 ul washing buffer and lysedthe by adding 5 ul ARCTURUS PICOPURE lysis buffer (APPLIED BIOSYSTEMS)and incubating at 56° C. for 20 min, 95° C. for 10 min.

The DNA of the single/three cells was amplified with 25 cycles of STA(95° C. for 10 min for initial polymerase activation, then 25 cycles of95° C. for 30s; 72° C. for 10 s; 65° C. for 1 min; 60° C. for 8 min; 65°C. for 3 min and 72° C. for 30s; and a final extension at 72° C. for 2min) using 50 nM primer concentration of 1200 target-specific forwardand tagged reverse primers.

The semi-nested PCR protocol involved three parallel secondamplification of a dilution of the first STAs product for 20 cycles ofSTA (95° C. for 10 min for initial polymerase activation, then 15 cyclesof 95° C. for 30s; 65° C. for 1 min; 60° C. for 5 min; 65° C. for 5 minand 72° C. for 30s; and a final extension at 72° C. for 2 min) usingreverse tag specific primer concentration of 1000 nM, and aconcentration of 60 nM for each of 400 target-specific nested forwardprimers. In the three parallel 400-plex reactions the total of 1200targets amplified in the first STA were thus amplified.

An aliquot of the STA products was then amplified by standard PCR for 15cycles with 1 uM of tag-specific forward and barcoded reverse primers togenerate barcoded sequencing libraries. An aliquot of each library wasmixed with libraries of different barcodes and purified using a spincolumn.

In this way, 1,200 primers were used in the single cell reactions; theprimers were designed to target SNPs found on chromosomes 1, 21 and X.The amplicons were then sequenced using an ILLUMINA GAIIX sequencer. Persample, approximately 3.9 million reads were generated by the sequencer,with 500,000 to 800,000 million reads mapping to the genome (74% to 94%of all reads per sample).

Relevant maternal and paternal genomic DNA samples from cell lines wereanalyzed using the same semi-nested 1200-plex assay pool with a similarprotocol with fewer cycles and 1200-plex second STA, and sequenced.

The sequencing data was analyzed using informatics methods disclosedherein and each of a set of ten unrelated males from a reference setwere determined to not be the biological father of the target individualfor each of the 45 cells.

DNA from Children from Previous Pregnancies in Maternal Blood

One difficulty to non-invasive prenatal paternity testing isdifferentiating fetal cells from the current pregnancy from fetal cellsfrom previous pregnancies. Some believe that genetic matter from priorpregnancies will go away after some time, but conclusive evidence hasnot been shown. In an embodiment of the present disclosure, it ispossible to determine fetal DNA present in the maternal blood ofpaternal origin (that is, DNA that the fetus inherited from the father)using the PARENTAL SUPPORT™ (PS) method, and the knowledge of thepaternal genome. This method may utilize phased parental geneticinformation. It is possible to phase the parental genotype from unphasedgenotypic information using grandparental genetic data (such as measuredgenetic data from a sperm from the grandfather), or genetic data fromother born children, or a sample of a miscarriage. One could also phaseunphased genetic information by way of a HapMap-based phasing, or ahaplotyping of paternal cells. Successful haplotyping has beendemonstrated by arresting cells at phase of mitosis when chromosomes aretight bundles and using microfluidics to put separate chromosomes inseparate wells. In another embodiment it is possible to use the phasedparental haplotypic data to detect the presence of more than one homologfrom the father, implying that the genetic material from more than onechild is present in the blood. By focusing on chromosomes that areexpected to be euploid in a fetus, one could rule out the possibilitythat the fetus was afflicted with a trisomy. Also, it is possible todetermine if the fetal DNA is not from the current father, in which caseone could use other methods such as the triple test to predict geneticabnormalities.

There may be other sources of fetal genetic material available viamethods other than a blood draw. In the case of the fetal geneticmaterial available in maternal blood, there are two main categories: (1)whole fetal cells, for example, nucleated fetal red blood cells orerythroblats, and (2) free floating fetal DNA. In the case of wholefetal cells, there is some evidence that fetal cells can persist inmaternal blood for an extended period of time such that it is possibleto isolate a cell from a pregnant woman that contains the DNA from achild or fetus from a prior pregnancy. There is also evidence that thefree floating fetal DNA is cleared from the system in a matter of weeks.One challenge is how to determine the identity of the individual whosegenetic material is contained in the cell, namely to ensure that themeasured genetic material is not from a fetus from a prior pregnancy. Inan embodiment of the present disclosure, the knowledge of the maternalgenetic material can be used to ensure that the genetic material inquestion is not maternal genetic material. There are a number of methodsto accomplish this end, including informatics based methods such asPARENTAL SUPPORT™, as described in this document or any of the patentsreferenced in this document.

In an embodiment of the present disclosure, the blood drawn from thepregnant mother may be separated into a fraction comprising freefloating fetal DNA, and a fraction comprising nucleated red blood cells.The free floating DNA may optionally be enriched, and the genotypicinformation of the DNA may be measured. From the measured genotypicinformation from the free floating DNA, the knowledge of the maternalgenotype may be used to determine aspects of the fetal genotype. Theseaspects may refer to ploidy state, and/or a set of allele identities.Then, individual nucleated cells that are presumably or possible fetalin origin may be genotyped using methods described elsewhere in thisdocument, and other referent patents, especially those mentioned in thisdocument. The knowledge of the maternal genome would allow one todetermine whether or not any given single blood cell is geneticallymaternal. And the aspects of the fetal genotype that were determined asdescribed above would allow one to determine if the single blood cell isgenetically derived from the fetus that is currently gestating. Inessence, this aspect of the present disclosure allows one to use thegenetic knowledge of the mother, and possibly the genetic informationfrom other related individuals, such as the father, along with themeasured genetic information from the free floating DNA found inmaternal blood to determine whether an isolated nucleated cell found inmaternal blood is either (a) genetically maternal, (b) genetically fromthe fetus currently gestating, or (c) genetically from a fetus from aprior pregnancy.

All patents, patent applications, and published references cited hereinare hereby incorporated by reference in their entirety. It will beappreciated that several of the above-disclosed and other features andfunctions, or alternatives thereof, may be desirably combined into manyother different systems or applications. Various presently unforeseen orunanticipated alternatives, modifications, variations, or improvementstherein may be subsequently made by those skilled in the art which arealso intended to be encompassed by the following claims.

What is claimed is:
 1. A method of amplifying target loci in a nucleicacid sample, the method comprising: performing multiplex polymerasechain reaction (PCR) on a nucleic acid sample comprising 1,000 targetloci in a single reaction volume, wherein the single reaction volumecomprises (i) 1,000 different target loci-specific PCR primer pairs or(ii) 1,000 different target loci-specific PCR primers and a universal ortag-specific PCR primer, wherein the concentration of each PCR primer inthe primer pairs or each target-specific PCR primer is 20 nM or less andthe length of an annealing step of the multiplex PCR is 10 minutes ormore, thereby producing amplified products comprising greater than 50%target amplicons that map to target loci.
 2. The method of claim 1,comprising performing universal amplification on nucleic acids in thesample prior to performing the multiplex PCR, wherein the universalamplification optionally comprises universal PCR, whole genomeamplification, ligation-mediated PCR, degenerate oligonucleotide primerPCR, or multiple displacement amplification.
 3. The method of claim 1,wherein the multiplex PCR comprises fully nested, semi-nested, orhemi-nested PCR; or wherein each primer pair comprises a forward and areverse primer in which the 3′ end of the forward and reverse primer isdesigned to hybridize to a region of DNA separated from a polymorphicsite in a target locus by a small number of bases, wherein the smallnumber is selected from the group consisting of 2, 3, 4, 5, 6, 7 to 10,11 to 15, or 16 to 20 bases.
 4. The method of claim 1, comprisingsimultaneously amplifying at least 5,000 distinct target loci.
 5. Themethod of claim 1, comprising simultaneously amplifying at least 10,000distinct target loci.
 6. The method of claim 1, wherein at least 90% ofthe amplified products map to the target loci.
 7. The method of claim 1,wherein the concentration of each primer in the primer pairs or eachtarget-specific primer is 10 nM or less.
 8. The method of claim 1,wherein the target loci are present in the human genome, or wherein thetarget loci comprise human single nucleotide polymorphisms.
 9. Themethod of claim 1, wherein the nucleic acid sample comprises DNA from afetus.
 10. The method of claim 1, wherein the nucleic acid samplecomprises maternal DNA from the pregnant mother of a fetus and fetalDNA, wherein the target loci comprise a human single nucleotidepolymorphism (SNP), and wherein the method comprises measuring theamount of one or more alleles at the target loci comprising a human SNP.11. The method of claim 1, wherein the nucleic acid sample comprises DNAfrom a tumor.
 12. The method of claim 1, wherein the nucleic acid samplecomprises DNA from an individual, and wherein the DNA comprises DNA froma cancer and DNA not from a cancer.
 13. The method of claim 1, whereinthe nucleic acid sample comprises DNA from a transplant.
 14. The methodof claim 1, wherein the length of the target amplicons is less than 100nucleotides.
 15. The method of claim 1, wherein the nucleic acid samplecomprises DNA from a single cell.
 16. The method of claim 1, wherein theannealing step comprises annealing at a temperature of 60° C. to 65° C.17. A method of amplifying target loci in a nucleic acid sample, themethod comprising: performing multiplex PCR on a nucleic acid samplecomprising DNA molecules having an average length of less than 200 basepairs and comprising 1,000 target loci in a single reaction volume,wherein the single reaction volume comprises (i) 1,000 different targetloci-specific PCR primer pairs or (ii) 1,000 different targetloci-specific PCR primers and a universal or tag-specific PCR primer,wherein the concentration of each PCR primer in the primer pairs or eachtarget-specific PCR primer is 20 nM or less and the length of anannealing step of the multiplex PCR is 10 minutes or more, therebyproducing amplified products comprising greater than 50% targetamplicons that are less than 100 nucleotides in length and map to targetloci.
 18. The method of claim 17, wherein each primer pair comprises aforward primer in which the 3′ end of the forward primer is designed tohybridize to a region of DNA separated from a polymorphic site in atarget locus by 2 to 20 bases.
 19. The method of claim 17, wherein eachprimer pair comprises a forward primer in which the 3′ end of theforward primer is designed to hybridize to a region of DNA separatedfrom a polymorphic site in a target locus by 2 to 10 bases.
 20. Themethod of claim 17, wherein the amplified products comprise greater than90% target amplicons.
 21. The method of claim 17, wherein the primerpairs are selected by eliminating one or more primers that form primerdimers.